fipy.meshes package¶

Submodules¶

fipy.meshes.abstractMesh module¶

class fipy.meshes.abstractMesh.AbstractMesh(communicator, _RepresentationClass=<class 'fipy.meshes.representations.abstractRepresentation._AbstractRepresentation'>, _TopologyClass=<class 'fipy.meshes.topologies.abstractTopology._AbstractTopology'>)¶

Bases: object

A class encapsulating all commonalities among meshes in FiPy.

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(other)¶

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(other)¶

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶: Topology properties

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

fipy.meshes.cylindricalGrid1D module¶

fipy.meshes.cylindricalGrid2D module¶

fipy.meshes.cylindricalNonUniformGrid1D module¶

1D Mesh

class fipy.meshes.cylindricalNonUniformGrid1D.CylindricalNonUniformGrid1D(dx=1.0, nx=None, origin=(0,), overlap=2, communicator=SerialPETScCommWrapper(), *args, **kwargs)¶

Bases: NonUniformGrid1D

Creates a 1D cylindrical grid mesh.

>>> mesh = CylindricalNonUniformGrid1D(nx = 3)
>>> print(mesh.cellCenters)
[[ 0.5  1.5  2.5]]

>>> mesh = CylindricalNonUniformGrid1D(dx = (1, 2, 3))
>>> print(mesh.cellCenters)
[[ 0.5  2.   4.5]]

>>> print(numerix.allclose(mesh.cellVolumes, (0.5, 4., 13.5))) 
True

>>> mesh = CylindricalNonUniformGrid1D(nx = 2, dx = (1, 2, 3))
Traceback (most recent call last):
...
IndexError: nx != len(dx)

>>> mesh = CylindricalNonUniformGrid1D(nx=2, dx=(1., 2.)) + ((1.,),)
>>> print(mesh.cellCenters)
[[ 1.5  3. ]]
>>> print(numerix.allclose(mesh.cellVolumes, (1.5, 6))) 
True

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

fipy.meshes.cylindricalNonUniformGrid2D module¶

2D rectangular Mesh

class fipy.meshes.cylindricalNonUniformGrid2D.CylindricalNonUniformGrid2D(dx=1.0, dy=1.0, nx=None, ny=None, origin=((0.0,), (0.0,)), overlap=2, communicator=SerialPETScCommWrapper(), *args, **kwargs)¶

Bases: NonUniformGrid2D

Creates a 2D cylindrical grid mesh with horizontal faces numbered first and then vertical faces.

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

extrude(extrudeFunc=<function Mesh2D.<lambda>>, layers=1)¶

This function returns a new 3D mesh. The 2D mesh is extruded using the extrudeFunc and the number of layers.

>>> from fipy.meshes.nonUniformGrid2D import NonUniformGrid2D
>>> print(NonUniformGrid2D(nx=2, ny=2).extrude(layers=2).cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]]

>>> from fipy.meshes.tri2D import Tri2D
>>> print(Tri2D().extrude(layers=2).cellCenters.allclose([[ 0.83333333, 0.5,        0.16666667, 0.5,       0.83333333, 0.5,
...                                                      0.16666667, 0.5       ],
...                                                       [ 0.5,        0.83333333, 0.5,        0.16666667, 0.5,        0.83333333,
...                                                      0.5,        0.16666667],
...                                                      [ 0.5,        0.5,        0.5,        0.5,        1.5,        1.5,        1.5,
...                                                      1.5       ]]))
True

Parameters:

extrudeFunc (function) – Takes the vertex coordinates and returns the displaced values
layers (int) – Number of layers in the extruded mesh (number of times extrudeFunc will be called)

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

fipy.meshes.cylindricalUniformGrid1D module¶

1D Mesh

class fipy.meshes.cylindricalUniformGrid1D.CylindricalUniformGrid1D(dx=1.0, nx=1, origin=(0,), overlap=2, communicator=SerialPETScCommWrapper(), *args, **kwargs)¶

Bases: UniformGrid1D

Creates a 1D cylindrical grid mesh.

>>> mesh = CylindricalUniformGrid1D(nx = 3)
>>> print(mesh.cellCenters)
[[ 0.5  1.5  2.5]]

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(other)¶

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

property faceCellIDs¶

property faceCenters¶

property faceNormals¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property vertexCoords¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

fipy.meshes.cylindricalUniformGrid2D module¶

2D cylindrical rectangular Mesh with constant spacing in x and constant spacing in y

class fipy.meshes.cylindricalUniformGrid2D.CylindricalUniformGrid2D(dx=1.0, dy=1.0, nx=1, ny=1, origin=((0,), (0,)), overlap=2, communicator=SerialPETScCommWrapper(), *args, **kwargs)¶

Bases: UniformGrid2D

Creates a 2D cylindrical grid in the radial and axial directions, appropriate for axial symmetry.

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(other)¶

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

property faceCellIDs¶

property faceCenters¶

property faceNormals¶

property faceVertexIDs¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property vertexCoords¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

fipy.meshes.factoryMeshes module¶

fipy.meshes.factoryMeshes.CylindricalGrid1D(dr=None, nr=None, Lr=None, dx=1.0, nx=None, Lx=None, origin=(0,), overlap=2, communicator=SerialPETScCommWrapper())¶

Create a 2D cylindrical mesh

Factory function to select between CylindricalUniformGrid1D and CylindricalNonUniformGrid1D. If Lr is specified the length of the domain is always Lr regardless of dr, unless dr is a list of spacings, in which case Lr will be the sum of dr.

Parameters:

dr (float) – Grid spacing in the radial direction. Alternative: dx.
nr (int) – Number of cells in the radial direction. Alternative: nx.
Lr (float) – Domain length in the radial direction. Alternative: Lx.
overlap (int) – the number of overlapping cells for parallel simulations. Generally 2 is adequate. Higher order equations or discretizations require more.
communicator (CommWrapper) – MPI communicator to use. Select serialComm to create a serial mesh when running in parallel; mostly used for test purposes. (default: parallelComm).

fipy.meshes.factoryMeshes.CylindricalGrid2D(dr=None, dz=None, nr=None, nz=None, Lr=None, Lz=None, dx=1.0, dy=1.0, nx=None, ny=None, Lx=None, Ly=None, origin=((0,), (0,)), overlap=2, communicator=SerialPETScCommWrapper())¶

Create a 2D cylindrical mesh

Factory function to select between CylindricalUniformGrid2D and CylindricalNonUniformGrid2D. If Lr is specified the length of the domain is always Lr regardless of dr, unless dr is a list of spacings, in which case Lr will be the sum of dr.

Parameters:

dr (float) – Grid spacing in the radial direction. Alternative: dx.
dz (float) – grid spacing in the vertical direction. Alternative: dy.
nr (int) – Number of cells in the radial direction. Alternative: nx.
nz (int) – Number of cells in the vertical direction. Alternative: ny.
Lr (float) – Domain length in the radial direction. Alternative: Lx.
Lz (float) – Domain length in the vertical direction. Alternative: Ly.
overlap (int) – the number of overlapping cells for parallel simulations. Generally 2 is adequate. Higher order equations or discretizations require more.
communicator (CommWrapper) – MPI communicator to use. Select serialComm to create a serial mesh when running in parallel; mostly used for test purposes. (default: parallelComm).

fipy.meshes.factoryMeshes.Grid1D(dx=1.0, nx=None, Lx=None, overlap=2, communicator=SerialPETScCommWrapper())¶

Create a 1D Cartesian mesh

Factory function to select between UniformGrid1D and NonUniformGrid1D. If Lx is specified the length of the domain is always Lx regardless of dx, unless dx is a list of spacings, in which case Lx will be the sum of dx and nx will be the count of dx.

Parameters:

dx (float) – Grid spacing in the horizontal direction
nx (int) – Number of cells in the horizontal direction
Lx (float) – Domain length in the horizontal direction
overlap (int) – Number of overlapping cells for parallel simulations. Generally 2 is adequate. Higher order equations or discretizations require more.
communicator (CommWrapper) – MPI communicator to use. Select serialComm to create a serial mesh when running in parallel; mostly used for test purposes. (default: parallelComm).

fipy.meshes.factoryMeshes.Grid2D(dx=1.0, dy=1.0, nx=None, ny=None, Lx=None, Ly=None, overlap=2, communicator=SerialPETScCommWrapper())¶

Create a 2D Cartesian mesh

Factory function to select between UniformGrid2D and NonUniformGrid2D. If L{x,y} is specified, the length of the domain is always L{x,y} regardless of d{x,y}, unless d{x,y} is a list of spacings, in which case L{x,y} will be the sum of d{x,y} and n{x,y} will be the count of d{x,y}.

>>> print(Grid2D(Lx=3., nx=2).dx)
1.5

Parameters:

dx (float) – Grid spacing in the horizontal direction
dy (float) – Grid spacing in the vertical direction
nx (int) – Number of cells in the horizontal direction
ny (int) – Number of cells in the vertical direction
Lx (float) – Domain length in the horizontal direction
Ly (float) – Domain length in the vertical direction
overlap (int) – Number of overlapping cells for parallel simulations. Generally 2 is adequate. Higher order equations or discretizations require more.
communicator (CommWrapper) – MPI communicator to use. Select serialComm to create a serial mesh when running in parallel; mostly used for test purposes. (default: parallelComm).

fipy.meshes.factoryMeshes.Grid3D(dx=1.0, dy=1.0, dz=1.0, nx=None, ny=None, nz=None, Lx=None, Ly=None, Lz=None, overlap=2, communicator=SerialPETScCommWrapper())¶

Create a 3D Cartesian mesh

Factory function to select between UniformGrid3D and NonUniformGrid3D. If L{x,y,z} is specified, the length of the domain is always L{x,y,z} regardless of d{x,y,z}, unless d{x,y,z} is a list of spacings, in which case L{x,y,z} will be the sum of d{x,y,z} and n{x,y,z} will be the count of d{x,y,z}.

Parameters:

dx (float) – Grid spacing in the horizontal direction
dy (float) – Grid spacing in the vertical direction
dz (float) – Grid spacing in the depth direction
nx (int) – Number of cells in the horizontal direction
ny (int) – Number of cells in the vertical direction
nz (int) – Number of cells in the depth direction
Lx (float) – Domain length in the horizontal direction
Ly (float) – Domain length in the vertical direction
Lz (float) – Domain length in the depth direction
overlap (int) – Number of overlapping cells for parallel simulations. Generally 2 is adequate. Higher order equations or discretizations require more.
communicator (CommWrapper) – MPI communicator to use. Select serialComm to create a serial mesh when running in parallel; mostly used for test purposes. (default: parallelComm).

fipy.meshes.factoryMeshes.SphericalGrid1D(dr=None, nr=None, Lr=None, dx=1.0, nx=None, Lx=None, origin=(0,), overlap=2, communicator=SerialPETScCommWrapper())¶

Create a 1D spherical mesh

Factory function to select between SphericalUniformGrid1D and SphericalNonUniformGrid1D. If Lr is specified the length of the domain is always Lr regardless of dr, unless dr is a list of spacings, in which case Lr will be the sum of dr.

Parameters:

dr (float) – Grid spacing in the radial direction. Alternative: dx.
nr (int) – Number of cells in the radial direction. Alternative: nx.
Lr (float) – Domain length in the radial direction. Alternative: Lx.
overlap (int) – the number of overlapping cells for parallel simulations. Generally 2 is adequate. Higher order equations or discretizations require more.
communicator (CommWrapper) – MPI communicator to use. Select serialComm to create a serial mesh when running in parallel; mostly used for test purposes. (default: parallelComm).

fipy.meshes.gmshMesh module¶

class fipy.meshes.gmshMesh.Gmsh2D(arg, coordDimensions=2, communicator=SerialPETScCommWrapper(), overlap=1, background=None)¶

Bases: Mesh2D

Construct a 2D Mesh using Gmsh

If called in parallel, the mesh will be partitioned based on the value of parallelComm.Nproc. If an MSH file is supplied, it must have been previously partitioned with the number of partitions matching parallelComm.Nproc.

>>> radius = 5.
>>> side = 4.
>>> squaredCircle = Gmsh2D('''
... // A mesh consisting of a square inside a circle inside a circle
...
... // define the basic dimensions of the mesh
...
... cellSize = 1;
... radius = %(radius)g;
... side = %(side)g;
...
... // define the compass points of the inner circle
...
... Point(1) = {0, 0, 0, cellSize};
... Point(2) = {-radius, 0, 0, cellSize};
... Point(3) = {0, radius, 0, cellSize};
... Point(4) = {radius, 0, 0, cellSize};
... Point(5) = {0, -radius, 0, cellSize};
...
... // define the compass points of the outer circle
...
... Point(6) = {-2*radius, 0, 0, cellSize};
... Point(7) = {0, 2*radius, 0, cellSize};
... Point(8) = {2*radius, 0, 0, cellSize};
... Point(9) = {0, -2*radius, 0, cellSize};
...
... // define the corners of the square
...
... Point(10) = {side/2, side/2, 0, cellSize/2};
... Point(11) = {-side/2, side/2, 0, cellSize/2};
... Point(12) = {-side/2, -side/2, 0, cellSize/2};
... Point(13) = {side/2, -side/2, 0, cellSize/2};
...
... // define the inner circle
...
... Circle(1) = {2, 1, 3};
... Circle(2) = {3, 1, 4};
... Circle(3) = {4, 1, 5};
... Circle(4) = {5, 1, 2};
...
... // define the outer circle
...
... Circle(5) = {6, 1, 7};
... Circle(6) = {7, 1, 8};
... Circle(7) = {8, 1, 9};
... Circle(8) = {9, 1, 6};
...
... // define the square
...
... Line(9) = {10, 13};
... Line(10) = {13, 12};
... Line(11) = {12, 11};
... Line(12) = {11, 10};
...
... // define the three boundaries
...
... Line Loop(1) = {1, 2, 3, 4};
... Line Loop(2) = {5, 6, 7, 8};
... Line Loop(3) = {9, 10, 11, 12};
...
... // define the three domains
...
... Plane Surface(1) = {2, 1};
... Plane Surface(2) = {1, 3};
... Plane Surface(3) = {3};
...
... // label the three domains
...
... // attention: if you use any "Physical" labels, you *must* label
... // all elements that correspond to FiPy Cells (Physical Surface in 2D
... // and Physical Volume in 3D) or Gmsh will not include them and FiPy
... // will not be able to include them in the Mesh.
...
... // note: if you do not use any labels, all Cells will be included.
...
... Physical Surface("Outer") = {1};
... Physical Surface("Middle") = {2};
... Physical Surface("Inner") = {3};
...
... // label the "north-west" part of the exterior boundary
...
... // note: you only need to label the Face elements
... // (Physical Line in 2D and Physical Surface in 3D) that correspond
... // to boundaries you are interested in. FiPy does not need them to
... // construct the Mesh.
...
... Physical Line("NW") = {5};
... ''' % locals()) 

It can be easier to specify certain domains and boundaries within Gmsh than it is to define the same domains and boundaries with FiPy expressions.

Here we compare obtaining the same Cells and Faces using FiPy’s parametric descriptions and Gmsh’s labels.

>>> x, y = squaredCircle.cellCenters 

>>> middle = ((x**2 + y**2 <= radius**2)
...           & ~((x > -side/2) & (x < side/2)
...               & (y > -side/2) & (y < side/2))) 

>>> print((middle == squaredCircle.physicalCells["Middle"]).all()) 
True

>>> X, Y = squaredCircle.faceCenters 

>>> NW = ((X**2 + Y**2 > (1.99*radius)**2)
...       & (X**2 + Y**2 < (2.01*radius)**2)
...       & (X <= 0) & (Y >= 0)) 

>>> print((NW == squaredCircle.physicalFaces["NW"]).all()) 
True

It is possible to direct Gmsh to give the mesh different densities in different locations

>>> geo = '''
... // A mesh consisting of a square
...
... // define the corners of the square
...
... Point(1) = {1, 1, 0, 1};
... Point(2) = {0, 1, 0, 1};
... Point(3) = {0, 0, 0, 1};
... Point(4) = {1, 0, 0, 1};
...
... // define the square
...
... Line(1) = {1, 2};
... Line(2) = {2, 3};
... Line(3) = {3, 4};
... Line(4) = {4, 1};
...
... // define the boundary
...
... Line Loop(1) = {1, 2, 3, 4};
...
... // define the domain
...
... Plane Surface(1) = {1};
... '''

>>> from fipy import CellVariable, numerix

>>> error = []
>>> bkg = None
>>> from builtins import range
>>> for refine in range(4):
...     square = Gmsh2D(geo, background=bkg) 
...     x, y = square.cellCenters 
...     bkg = CellVariable(mesh=square, value=abs(x / 4) + 0.01) 
...     error.append(((2 * numerix.sqrt(square.cellVolumes) / bkg - 1)**2).cellVolumeAverage) 

Check that the mesh is (semi)monotonically approaching the desired density (the first step may increase, depending on the number of partitions)

>>> print(numerix.greater(error[:-1], error[1:]).all()) 
True

and that the final density is close enough to the desired density

>>> print(error[-1] < 0.02) 
True

The initial mesh doesn’t have to be from Gmsh

>>> from fipy import Tri2D

>>> trisquare = Tri2D(nx=1, ny=1)
>>> x, y = trisquare.cellCenters
>>> bkg = CellVariable(mesh=trisquare, value=abs(x / 4) + 0.01)
>>> std1 = (numerix.sqrt(2 * trisquare.cellVolumes) / bkg).std()

>>> square = Gmsh2D(geo, background=bkg) 
>>> x, y = square.cellCenters 
>>> bkg = CellVariable(mesh=square, value=abs(x / 4) + 0.01) 
>>> std2 = (numerix.sqrt(2 * square.cellVolumes) / bkg).std() 

>>> print(std1 > std2) 
True

Parameters:

arg (str) – (i) the path to an MSH file, (ii) a path to a Gmsh geometry (.geo) file, or (iii) a Gmsh geometry script
coordDimensions (int) – Dimension of shapes
overlap (int) – The number of overlapping cells for parallel simulations. Generally 1 is adequate. Higher order equations or discretizations require more. If overlap is greater than one, communication reverts to serial, as Gmsh only provides one layer of ghost cells.
background (CellVariable) – Specifies the desired characteristic lengths of the mesh cells

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

extrude(extrudeFunc=<function Mesh2D.<lambda>>, layers=1)¶

This function returns a new 3D mesh. The 2D mesh is extruded using the extrudeFunc and the number of layers.

>>> from fipy.meshes.nonUniformGrid2D import NonUniformGrid2D
>>> print(NonUniformGrid2D(nx=2, ny=2).extrude(layers=2).cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]]

>>> from fipy.meshes.tri2D import Tri2D
>>> print(Tri2D().extrude(layers=2).cellCenters.allclose([[ 0.83333333, 0.5,        0.16666667, 0.5,       0.83333333, 0.5,
...                                                      0.16666667, 0.5       ],
...                                                       [ 0.5,        0.83333333, 0.5,        0.16666667, 0.5,        0.83333333,
...                                                      0.5,        0.16666667],
...                                                      [ 0.5,        0.5,        0.5,        0.5,        1.5,        1.5,        1.5,
...                                                      1.5       ]]))
True

Parameters:

extrudeFunc (function) – Takes the vertex coordinates and returns the displaced values
layers (int) – Number of layers in the extruded mesh (number of times extrudeFunc will be called)

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

class fipy.meshes.gmshMesh.Gmsh2DIn3DSpace(arg, communicator=SerialPETScCommWrapper(), overlap=1, background=None)¶

Bases: Gmsh2D

Create a topologically 2D Mesh in 3D coordinates using Gmsh

If called in parallel, the mesh will be partitioned based on the value of parallelComm.Nproc. If an MSH file is supplied, it must have been previously partitioned with the number of partitions matching parallelComm.Nproc.

Parameters:

arg (str) – (i) the path to an MSH file, (ii) a path to a Gmsh geometry (.geo) file, or (iii) a Gmsh geometry script
coordDimensions (int) – Dimension of shapes
overlap (int) – The number of overlapping cells for parallel simulations. Generally 1 is adequate. Higher order equations or discretizations require more. If overlap is greater than one, communication reverts to serial, as Gmsh only provides one layer of ghost cells.
background (CellVariable) – Specifies the desired characteristic lengths of the mesh cells

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

extrude(extrudeFunc=<function Mesh2D.<lambda>>, layers=1)¶

This function returns a new 3D mesh. The 2D mesh is extruded using the extrudeFunc and the number of layers.

>>> from fipy.meshes.nonUniformGrid2D import NonUniformGrid2D
>>> print(NonUniformGrid2D(nx=2, ny=2).extrude(layers=2).cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]]

>>> from fipy.meshes.tri2D import Tri2D
>>> print(Tri2D().extrude(layers=2).cellCenters.allclose([[ 0.83333333, 0.5,        0.16666667, 0.5,       0.83333333, 0.5,
...                                                      0.16666667, 0.5       ],
...                                                       [ 0.5,        0.83333333, 0.5,        0.16666667, 0.5,        0.83333333,
...                                                      0.5,        0.16666667],
...                                                      [ 0.5,        0.5,        0.5,        0.5,        1.5,        1.5,        1.5,
...                                                      1.5       ]]))
True

Parameters:

extrudeFunc (function) – Takes the vertex coordinates and returns the displaced values
layers (int) – Number of layers in the extruded mesh (number of times extrudeFunc will be called)

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

class fipy.meshes.gmshMesh.Gmsh3D(arg, communicator=SerialPETScCommWrapper(), overlap=1, background=None)¶

Bases: Mesh

Create a 3D Mesh using Gmsh

If called in parallel, the mesh will be partitioned based on the value of parallelComm.Nproc. If an MSH file is supplied, it must have been previously partitioned with the number of partitions matching parallelComm.Nproc.

Parameters:

arg (str) – (i) the path to an MSH file, (ii) a path to a Gmsh geometry (.geo) file, or (iii) a Gmsh geometry script
overlap (int) – The number of overlapping cells for parallel simulations. Generally 1 is adequate. Higher order equations or discretizations require more. If overlap is greater than one, communication reverts to serial, as Gmsh only provides one layer of ghost cells.
background (CellVariable) – Specifies the desired characteristic lengths of the mesh cells

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

class fipy.meshes.gmshMesh.GmshGrid2D(dx=1.0, dy=1.0, nx=1, ny=None, coordDimensions=2, communicator=SerialPETScCommWrapper(), overlap=1)¶

Bases: Gmsh2D

Should serve as a drop-in replacement for Grid2D

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

extrude(extrudeFunc=<function Mesh2D.<lambda>>, layers=1)¶

This function returns a new 3D mesh. The 2D mesh is extruded using the extrudeFunc and the number of layers.

>>> from fipy.meshes.nonUniformGrid2D import NonUniformGrid2D
>>> print(NonUniformGrid2D(nx=2, ny=2).extrude(layers=2).cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]]

>>> from fipy.meshes.tri2D import Tri2D
>>> print(Tri2D().extrude(layers=2).cellCenters.allclose([[ 0.83333333, 0.5,        0.16666667, 0.5,       0.83333333, 0.5,
...                                                      0.16666667, 0.5       ],
...                                                       [ 0.5,        0.83333333, 0.5,        0.16666667, 0.5,        0.83333333,
...                                                      0.5,        0.16666667],
...                                                      [ 0.5,        0.5,        0.5,        0.5,        1.5,        1.5,        1.5,
...                                                      1.5       ]]))
True

Parameters:

extrudeFunc (function) – Takes the vertex coordinates and returns the displaced values
layers (int) – Number of layers in the extruded mesh (number of times extrudeFunc will be called)

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

class fipy.meshes.gmshMesh.GmshGrid3D(dx=1.0, dy=1.0, dz=1.0, nx=1, ny=None, nz=None, communicator=SerialPETScCommWrapper(), overlap=1)¶

Bases: Gmsh3D

Should serve as a drop-in replacement for Grid3D

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

fipy.meshes.gmshMesh.openMSHFile(name, dimensions=None, coordDimensions=None, communicator=SerialPETScCommWrapper(), overlap=1, mode='r', background=None)¶

Open a Gmsh MSH file

Parameters:

filename (str) – Gmsh output file
dimensions (int) – Dimension of mesh
coordDimensions (int) – Dimension of shapes
overlap (int) – The number of overlapping cells for parallel simulations. Generally 1 is adequate. Higher order equations or discretizations require more. If overlap is greater than one, communication reverts to serial, as Gmsh only provides one layer of ghost cells.
mode (str) – Beginning with r for reading and w for writing. The file will be created if it doesn’t exist when opened for writing; it will be truncated when opened for writing. Add a b to the mode for binary files.
background (CellVariable) – Specifies the desired characteristic lengths of the mesh cells

fipy.meshes.gmshMesh.openPOSFile(name, communicator=SerialPETScCommWrapper(), mode='w')¶: Open a Gmsh POS post-processing file

fipy.meshes.grid1D module¶

fipy.meshes.grid2D module¶

fipy.meshes.grid3D module¶

fipy.meshes.mesh module¶

class fipy.meshes.mesh.Mesh(vertexCoords, faceVertexIDs, cellFaceIDs, communicator=SerialPETScCommWrapper(), _RepresentationClass=<class 'fipy.meshes.representations.meshRepresentation._MeshRepresentation'>, _TopologyClass=<class 'fipy.meshes.topologies.meshTopology._MeshTopology'>)¶

Bases: AbstractMesh

Generic mesh class using numerix to do the calculations

Meshes contain cells, faces, and vertices.

This is built for a non-mixed element mesh.

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

exception fipy.meshes.mesh.MeshAdditionError¶

Bases: Exception

__cause__¶: exception cause

__context__¶: exception context

__delattr__(name, /)¶: Implement delattr(self, name).

__getattribute__(name, /)¶: Return getattr(self, name).

__reduce__()¶: Helper for pickle.

__repr__()¶: Return repr(self).

__setattr__(name, value, /)¶: Implement setattr(self, name, value).

__setstate__()¶

__str__()¶: Return str(self).

__suppress_context__¶

__traceback__¶

add_note()¶: Exception.add_note(note) – add a note to the exception

args¶

with_traceback()¶: Exception.with_traceback(tb) – set self.__traceback__ to tb and return self.

fipy.meshes.mesh1D module¶

Generic mesh class using numerix to do the calculations

Meshes contain cells, faces, and vertices.

This is built for a non-mixed element mesh.

class fipy.meshes.mesh1D.Mesh1D(vertexCoords, faceVertexIDs, cellFaceIDs, communicator=SerialPETScCommWrapper(), _RepresentationClass=<class 'fipy.meshes.representations.meshRepresentation._MeshRepresentation'>, _TopologyClass=<class 'fipy.meshes.topologies.meshTopology._Mesh1DTopology'>)¶

Bases: Mesh

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

fipy.meshes.mesh2D module¶

Generic mesh class using numerix to do the calculations

Meshes contain cells, faces, and vertices.

This is built for a non-mixed element mesh.

class fipy.meshes.mesh2D.Mesh2D(vertexCoords, faceVertexIDs, cellFaceIDs, communicator=SerialPETScCommWrapper(), _RepresentationClass=<class 'fipy.meshes.representations.meshRepresentation._MeshRepresentation'>, _TopologyClass=<class 'fipy.meshes.topologies.meshTopology._Mesh2DTopology'>)¶

Bases: Mesh

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

extrude(extrudeFunc=<function Mesh2D.<lambda>>, layers=1)¶

This function returns a new 3D mesh. The 2D mesh is extruded using the extrudeFunc and the number of layers.

>>> from fipy.meshes.nonUniformGrid2D import NonUniformGrid2D
>>> print(NonUniformGrid2D(nx=2, ny=2).extrude(layers=2).cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]]

>>> from fipy.meshes.tri2D import Tri2D
>>> print(Tri2D().extrude(layers=2).cellCenters.allclose([[ 0.83333333, 0.5,        0.16666667, 0.5,       0.83333333, 0.5,
...                                                      0.16666667, 0.5       ],
...                                                       [ 0.5,        0.83333333, 0.5,        0.16666667, 0.5,        0.83333333,
...                                                      0.5,        0.16666667],
...                                                      [ 0.5,        0.5,        0.5,        0.5,        1.5,        1.5,        1.5,
...                                                      1.5       ]]))
True

Parameters:

extrudeFunc (function) – Takes the vertex coordinates and returns the displaced values
layers (int) – Number of layers in the extruded mesh (number of times extrudeFunc will be called)

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

fipy.meshes.nonUniformGrid1D module¶

1D Mesh

class fipy.meshes.nonUniformGrid1D.NonUniformGrid1D(dx=1.0, nx=None, overlap=2, communicator=SerialPETScCommWrapper(), _BuilderClass=<class 'fipy.meshes.builders.grid1DBuilder._NonuniformGrid1DBuilder'>, _RepresentationClass=<class 'fipy.meshes.representations.gridRepresentation._Grid1DRepresentation'>, _TopologyClass=<class 'fipy.meshes.topologies.gridTopology._Grid1DTopology'>)¶

Bases: Mesh1D

Creates a 1D grid mesh.

>>> mesh = NonUniformGrid1D(nx = 3)
>>> print(mesh.cellCenters)
[[ 0.5  1.5  2.5]]

>>> mesh = NonUniformGrid1D(dx = (1, 2, 3))
>>> print(mesh.cellCenters)
[[ 0.5  2.   4.5]]

>>> mesh = NonUniformGrid1D(nx = 2, dx = (1, 2, 3))
Traceback (most recent call last):
...
IndexError: nx != len(dx)

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

fipy.meshes.nonUniformGrid2D module¶

2D rectangular Mesh

class fipy.meshes.nonUniformGrid2D.NonUniformGrid2D(dx=1.0, dy=1.0, nx=None, ny=None, overlap=2, communicator=SerialPETScCommWrapper(), _RepresentationClass=<class 'fipy.meshes.representations.gridRepresentation._Grid2DRepresentation'>, _TopologyClass=<class 'fipy.meshes.topologies.gridTopology._Grid2DTopology'>)¶

Bases: Mesh2D

Creates a 2D grid mesh with horizontal faces numbered first and then vertical faces.

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

extrude(extrudeFunc=<function Mesh2D.<lambda>>, layers=1)¶

This function returns a new 3D mesh. The 2D mesh is extruded using the extrudeFunc and the number of layers.

>>> from fipy.meshes.nonUniformGrid2D import NonUniformGrid2D
>>> print(NonUniformGrid2D(nx=2, ny=2).extrude(layers=2).cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]]

>>> from fipy.meshes.tri2D import Tri2D
>>> print(Tri2D().extrude(layers=2).cellCenters.allclose([[ 0.83333333, 0.5,        0.16666667, 0.5,       0.83333333, 0.5,
...                                                      0.16666667, 0.5       ],
...                                                       [ 0.5,        0.83333333, 0.5,        0.16666667, 0.5,        0.83333333,
...                                                      0.5,        0.16666667],
...                                                      [ 0.5,        0.5,        0.5,        0.5,        1.5,        1.5,        1.5,
...                                                      1.5       ]]))
True

Parameters:

extrudeFunc (function) – Takes the vertex coordinates and returns the displaced values
layers (int) – Number of layers in the extruded mesh (number of times extrudeFunc will be called)

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

fipy.meshes.nonUniformGrid3D module¶

class fipy.meshes.nonUniformGrid3D.NonUniformGrid3D(dx=1.0, dy=1.0, dz=1.0, nx=None, ny=None, nz=None, overlap=2, communicator=SerialPETScCommWrapper(), _RepresentationClass=<class 'fipy.meshes.representations.gridRepresentation._Grid3DRepresentation'>, _TopologyClass=<class 'fipy.meshes.topologies.gridTopology._Grid3DTopology'>)¶

Bases: Mesh

3D rectangular-prism Mesh

X axis runs from left to right. Y axis runs from bottom to top. Z axis runs from front to back.

Numbering System:

Vertices: Numbered in the usual way. X coordinate changes most quickly, then Y, then Z.

Cells: Same numbering system as vertices.

Faces: XY faces numbered first, then XZ faces, then YZ faces. Within each subcategory, it is numbered in the usual way.

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

fipy.meshes.periodicGrid1D module¶

Periodic 1D Mesh

class fipy.meshes.periodicGrid1D.PeriodicGrid1D(dx=1.0, nx=None, overlap=2, *args, **kwargs)¶

Bases: NonUniformGrid1D

Creates a Periodic grid mesh.

>>> mesh = PeriodicGrid1D(dx = (1, 2, 3))

>>> print(numerix.allclose(numerix.nonzero(mesh.exteriorFaces)[0],
...                        [3])) 
True

>>> print(numerix.allclose(mesh.faceCellIDs.filled(-999),
...                        [[2, 0, 1, 2],
...                         [0, 1, 2, -999]])) 
True

>>> print(numerix.allclose(mesh._cellDistances,
...                        [ 2., 1.5, 2.5, 1.5])) 
True

>>> print(numerix.allclose(mesh._cellToCellDistances,
...                        [[ 2.,   1.5,  2.5],
...                         [ 1.5,  2.5,  2. ]])) 
True

>>> print(numerix.allclose(mesh.faceNormals,
...                        [[ 1.,  1.,  1.,  1.]])) 
True

>>> print(numerix.allclose(mesh._cellVertexIDs,
...                        [[1, 2, 2],
...                        [0, 1, 0]])) 
True

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶: Defined outside of a geometry class since we need the CellVariable version of cellCenters; that is, the cellCenters defined in fipy.meshes.mesh and not in any geometry (since a CellVariable requires a reference to a mesh).

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

fipy.meshes.periodicGrid2D module¶

2D periodic rectangular Mesh

class fipy.meshes.periodicGrid2D.PeriodicGrid2D(dx=1.0, dy=1.0, nx=None, ny=None, overlap=2, communicator=SerialPETScCommWrapper(), *args, **kwargs)¶

Bases: _BasePeriodicGrid2D

Creates a periodic 2D grid mesh with horizontal faces numbered first and then vertical faces. Vertices and cells are numbered in the usual way.

>>> from fipy import numerix

>>> mesh = PeriodicGrid2D(dx = 1., dy = 0.5, nx = 2, ny = 2)

>>> print(numerix.allclose(numerix.nonzero(mesh.exteriorFaces)[0],
...                        [ 4,  5,  8, 11]))  
True

>>> print(numerix.allclose(mesh.faceCellIDs.filled(-1),
...                        [[2, 3, 0, 1, 2, 3, 1, 0, 1, 3, 2, 3],
...                         [0, 1, 2, 3, -1, -1, 0, 1, -1, 2, 3, -1]])) 
True

>>> print(numerix.allclose(mesh._cellDistances,
...                        [ 0.5, 0.5, 0.5, 0.5, 0.25, 0.25, 1., 1., 0.5, 1., 1., 0.5])) 
True

>>> print(numerix.allclose(mesh.cellFaceIDs,
...                        [[0, 1, 2, 3],
...                         [7, 6, 10, 9],
...                         [2, 3, 0, 1],
...                         [6, 7, 9, 10]])) 
True

>>> print(numerix.allclose(mesh._cellToCellDistances,
...                        [[ 0.5, 0.5, 0.5, 0.5],
...                         [ 1., 1., 1., 1. ],
...                         [ 0.5, 0.5, 0.5, 0.5],
...                         [ 1., 1., 1., 1. ]])) 
True

>>> normals = [[0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1],
...            [1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0]]

>>> print(numerix.allclose(mesh.faceNormals, normals)) 
True

>>> print(numerix.allclose(mesh._cellVertexIDs,
...                        [[4, 5, 7, 8],
...                         [3, 4, 6, 7],
...                         [1, 2, 4, 5],
...                         [0, 1, 3, 4]])) 
True

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

extrude(extrudeFunc=<function Mesh2D.<lambda>>, layers=1)¶

This function returns a new 3D mesh. The 2D mesh is extruded using the extrudeFunc and the number of layers.

>>> from fipy.meshes.nonUniformGrid2D import NonUniformGrid2D
>>> print(NonUniformGrid2D(nx=2, ny=2).extrude(layers=2).cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]]

>>> from fipy.meshes.tri2D import Tri2D
>>> print(Tri2D().extrude(layers=2).cellCenters.allclose([[ 0.83333333, 0.5,        0.16666667, 0.5,       0.83333333, 0.5,
...                                                      0.16666667, 0.5       ],
...                                                       [ 0.5,        0.83333333, 0.5,        0.16666667, 0.5,        0.83333333,
...                                                      0.5,        0.16666667],
...                                                      [ 0.5,        0.5,        0.5,        0.5,        1.5,        1.5,        1.5,
...                                                      1.5       ]]))
True

Parameters:

extrudeFunc (function) – Takes the vertex coordinates and returns the displaced values
layers (int) – Number of layers in the extruded mesh (number of times extrudeFunc will be called)

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

class fipy.meshes.periodicGrid2D.PeriodicGrid2DLeftRight(dx=1.0, dy=1.0, nx=None, ny=None, overlap=2, communicator=SerialPETScCommWrapper(), *args, **kwargs)¶

Bases: _BasePeriodicGrid2D

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

extrude(extrudeFunc=<function Mesh2D.<lambda>>, layers=1)¶

This function returns a new 3D mesh. The 2D mesh is extruded using the extrudeFunc and the number of layers.

>>> from fipy.meshes.nonUniformGrid2D import NonUniformGrid2D
>>> print(NonUniformGrid2D(nx=2, ny=2).extrude(layers=2).cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]]

>>> from fipy.meshes.tri2D import Tri2D
>>> print(Tri2D().extrude(layers=2).cellCenters.allclose([[ 0.83333333, 0.5,        0.16666667, 0.5,       0.83333333, 0.5,
...                                                      0.16666667, 0.5       ],
...                                                       [ 0.5,        0.83333333, 0.5,        0.16666667, 0.5,        0.83333333,
...                                                      0.5,        0.16666667],
...                                                      [ 0.5,        0.5,        0.5,        0.5,        1.5,        1.5,        1.5,
...                                                      1.5       ]]))
True

Parameters:

extrudeFunc (function) – Takes the vertex coordinates and returns the displaced values
layers (int) – Number of layers in the extruded mesh (number of times extrudeFunc will be called)

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

class fipy.meshes.periodicGrid2D.PeriodicGrid2DTopBottom(dx=1.0, dy=1.0, nx=None, ny=None, overlap=2, communicator=SerialPETScCommWrapper(), *args, **kwargs)¶

Bases: _BasePeriodicGrid2D

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

extrude(extrudeFunc=<function Mesh2D.<lambda>>, layers=1)¶

This function returns a new 3D mesh. The 2D mesh is extruded using the extrudeFunc and the number of layers.

>>> from fipy.meshes.nonUniformGrid2D import NonUniformGrid2D
>>> print(NonUniformGrid2D(nx=2, ny=2).extrude(layers=2).cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]]

>>> from fipy.meshes.tri2D import Tri2D
>>> print(Tri2D().extrude(layers=2).cellCenters.allclose([[ 0.83333333, 0.5,        0.16666667, 0.5,       0.83333333, 0.5,
...                                                      0.16666667, 0.5       ],
...                                                       [ 0.5,        0.83333333, 0.5,        0.16666667, 0.5,        0.83333333,
...                                                      0.5,        0.16666667],
...                                                      [ 0.5,        0.5,        0.5,        0.5,        1.5,        1.5,        1.5,
...                                                      1.5       ]]))
True

Parameters:

extrudeFunc (function) – Takes the vertex coordinates and returns the displaced values
layers (int) – Number of layers in the extruded mesh (number of times extrudeFunc will be called)

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

fipy.meshes.periodicGrid3D module¶

3D periodic rectangular Mesh

class fipy.meshes.periodicGrid3D.PeriodicGrid3D(dx=1.0, dy=1.0, dz=1.0, nx=None, ny=None, nz=None, overlap=2, communicator=SerialPETScCommWrapper(), *args, **kwargs)¶

Bases: _BasePeriodicGrid3D

Creates a periodic 3D grid mesh with horizontal faces numbered first and then vertical faces. Vertices and cells are numbered in the usual way.

>>> from fipy import numerix

>>> mesh = PeriodicGrid3D(dx=1., dy=0.5, dz=2., nx=2, ny=2, nz=1)
>>> print(numerix.allclose(numerix.nonzero(mesh.exteriorFaces)[0],
...                        [4, 5, 6, 7, 12, 13, 16, 19]))  
True

>>> print(numerix.allclose(mesh.faceCellIDs.filled(-1),
...                        [[0, 1, 2, 3, 0, 1, 2, 3, 2, 3,
...                          0, 1, 2, 3, 1, 0, 1, 3, 2, 3],
...                         [0, 1, 2, 3, -1, -1, -1, -1, 0, 1,
...                          2, 3, -1, -1, 0, 1, -1, 2, 3, -1]])) 
True

>>> print(numerix.allclose(mesh._cellDistances,
...                        [2., 2., 2., 2., 1., 1., 1., 1., 0.5, 0.5,
...                         0.5, 0.5, 0.25, 0.25, 1., 1., 0.5, 1., 1., 0.5])) 
True

>>> print(numerix.allclose(mesh.cellFaceIDs,
...                        [[14, 15, 17, 18],
...                         [15, 14, 18, 17],
...                         [8, 9, 10, 11],
...                         [10, 11, 8, 9],
...                         [0, 1, 2, 3],
...                         [0, 1, 2, 3]])) 
True

>>> print(numerix.allclose(mesh._cellToCellDistances,
...                        [[1., 1., 1., 1.],
...                         [1., 1., 1., 1.],
...                         [0.5, 0.5, 0.5, 0.5],
...                         [0.5, 0.5, 0.5, 0.5],
...                         [2., 2., 2., 2.],
...                         [2., 2., 2., 2.]])) 
True

>>> normals = [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1],
...            [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0],
...            [1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]

>>> print(numerix.allclose(mesh.faceNormals, normals)) 
True

>>> print(numerix.allclose(mesh._cellVertexIDs,
...                        [[13, 14, 16, 17],
...                         [12, 13, 15, 16],
...                         [10, 11, 13, 14],
...                         [9, 10, 12, 13],
...                         [4, 5, 7, 8],
...                         [3, 4, 6, 7],
...                         [1, 2, 4, 5],
...                         [0, 1, 3, 4]])) 
True

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

class fipy.meshes.periodicGrid3D.PeriodicGrid3DFrontBack(dx=1.0, dy=1.0, dz=1.0, nx=None, ny=None, nz=None, overlap=2, communicator=SerialPETScCommWrapper(), *args, **kwargs)¶

Bases: _BasePeriodicGrid3D

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

class fipy.meshes.periodicGrid3D.PeriodicGrid3DLeftRight(dx=1.0, dy=1.0, dz=1.0, nx=None, ny=None, nz=None, overlap=2, communicator=SerialPETScCommWrapper(), *args, **kwargs)¶

Bases: _BasePeriodicGrid3D

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

class fipy.meshes.periodicGrid3D.PeriodicGrid3DLeftRightFrontBack(dx=1.0, dy=1.0, dz=1.0, nx=None, ny=None, nz=None, overlap=2, communicator=SerialPETScCommWrapper(), *args, **kwargs)¶

Bases: _BasePeriodicGrid3D

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

class fipy.meshes.periodicGrid3D.PeriodicGrid3DLeftRightTopBottom(dx=1.0, dy=1.0, dz=1.0, nx=None, ny=None, nz=None, overlap=2, communicator=SerialPETScCommWrapper(), *args, **kwargs)¶

Bases: _BasePeriodicGrid3D

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

class fipy.meshes.periodicGrid3D.PeriodicGrid3DTopBottom(dx=1.0, dy=1.0, dz=1.0, nx=None, ny=None, nz=None, overlap=2, communicator=SerialPETScCommWrapper(), *args, **kwargs)¶

Bases: _BasePeriodicGrid3D

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

class fipy.meshes.periodicGrid3D.PeriodicGrid3DTopBottomFrontBack(dx=1.0, dy=1.0, dz=1.0, nx=None, ny=None, nz=None, overlap=2, communicator=SerialPETScCommWrapper(), *args, **kwargs)¶

Bases: _BasePeriodicGrid3D

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

fipy.meshes.skewedGrid2D module¶

class fipy.meshes.skewedGrid2D.SkewedGrid2D(dx=1.0, dy=1.0, nx=None, ny=1, rand=0, *args, **kwargs)¶

Bases: Mesh2D

Creates a 2D grid mesh with horizontal faces numbered first and then vertical faces. The points are skewed by a random amount (between rand and -rand) in the X and Y directions.

Note

This Mesh only operates in serial

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

extrude(extrudeFunc=<function Mesh2D.<lambda>>, layers=1)¶

This function returns a new 3D mesh. The 2D mesh is extruded using the extrudeFunc and the number of layers.

>>> from fipy.meshes.nonUniformGrid2D import NonUniformGrid2D
>>> print(NonUniformGrid2D(nx=2, ny=2).extrude(layers=2).cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]]

>>> from fipy.meshes.tri2D import Tri2D
>>> print(Tri2D().extrude(layers=2).cellCenters.allclose([[ 0.83333333, 0.5,        0.16666667, 0.5,       0.83333333, 0.5,
...                                                      0.16666667, 0.5       ],
...                                                       [ 0.5,        0.83333333, 0.5,        0.16666667, 0.5,        0.83333333,
...                                                      0.5,        0.16666667],
...                                                      [ 0.5,        0.5,        0.5,        0.5,        1.5,        1.5,        1.5,
...                                                      1.5       ]]))
True

Parameters:

extrudeFunc (function) – Takes the vertex coordinates and returns the displaced values
layers (int) – Number of layers in the extruded mesh (number of times extrudeFunc will be called)

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property physicalShape¶: Return physical dimensions of Grid2D.

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property shape¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

fipy.meshes.sphericalNonUniformGrid1D module¶

1D Mesh

class fipy.meshes.sphericalNonUniformGrid1D.SphericalNonUniformGrid1D(dx=1.0, nx=None, origin=(0,), overlap=2, communicator=SerialPETScCommWrapper(), *args, **kwargs)¶

Bases: NonUniformGrid1D

Creates a 1D spherical grid mesh.

>>> mesh = SphericalNonUniformGrid1D(nx = 3)
>>> print(mesh.cellCenters)
[[ 0.5  1.5  2.5]]

>>> mesh = SphericalNonUniformGrid1D(dx = (1, 2, 3))
>>> print(mesh.cellCenters)
[[ 0.5  2.   4.5]]

>>> print(numerix.allclose(mesh.cellVolumes, (0.5, 13., 94.5))) 
True

>>> mesh = SphericalNonUniformGrid1D(nx = 2, dx = (1, 2, 3))
Traceback (most recent call last):
...
IndexError: nx != len(dx)

>>> mesh = SphericalNonUniformGrid1D(nx=2, dx=(1., 2.)) + ((1.,),)
>>> print(mesh.cellCenters)
[[ 1.5  3. ]]
>>> print(numerix.allclose(mesh.cellVolumes, (3.5, 28))) 
True

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

fipy.meshes.sphericalUniformGrid1D module¶

1D Mesh

class fipy.meshes.sphericalUniformGrid1D.SphericalUniformGrid1D(dx=1.0, nx=1, origin=(0,), overlap=2, communicator=SerialPETScCommWrapper(), *args, **kwargs)¶

Bases: UniformGrid1D

Creates a 1D spherical grid mesh.

>>> mesh = SphericalUniformGrid1D(nx = 3)
>>> print(mesh.cellCenters)
[[ 0.5  1.5  2.5]]

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(other)¶

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

property faceCellIDs¶

property faceCenters¶

property faceNormals¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property vertexCoords¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

fipy.meshes.test module¶

Test implementation of the mesh

fipy.meshes.tri2D module¶

class fipy.meshes.tri2D.Tri2D(dx=1.0, dy=1.0, nx=1, ny=1, _RepresentationClass=<class 'fipy.meshes.representations.gridRepresentation._Grid2DRepresentation'>, _TopologyClass=<class 'fipy.meshes.topologies.meshTopology._Mesh2DTopology'>)¶

Bases: Mesh2D

This class creates a mesh made out of triangles. It does this by starting with a standard Cartesian mesh (Grid2D) and dividing each cell in that mesh (hereafter referred to as a “box”) into four equal parts with the dividing lines being the diagonals.

Creates a 2D triangular mesh with horizontal faces numbered first then vertical faces, then diagonal faces. Vertices are numbered starting with the vertices at the corners of boxes and then the vertices at the centers of boxes. Cells on the right of boxes are numbered first, then cells on the top of boxes, then cells on the left of boxes, then cells on the bottom of boxes. Within each of the “sub-categories” in the above, the vertices, cells and faces are numbered in the usual way.

Parameters:

dx (float) – The X and Y dimensions of each “box”. If dx <> dy, the line segments connecting the cell centers will not be orthogonal to the faces.
dy (float) – The X and Y dimensions of each “box”. If dx <> dy, the line segments connecting the cell centers will not be orthogonal to the faces.
nx (int) – The number of boxes in the X direction and the Y direction. The total number of boxes will be equal to nx * ny, and the total number of cells will be equal to 4 * nx * ny.
ny (int) – The number of boxes in the X direction and the Y direction. The total number of boxes will be equal to nx * ny, and the total number of cells will be equal to 4 * nx * ny.

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

extrude(extrudeFunc=<function Mesh2D.<lambda>>, layers=1)¶

This function returns a new 3D mesh. The 2D mesh is extruded using the extrudeFunc and the number of layers.

>>> from fipy.meshes.nonUniformGrid2D import NonUniformGrid2D
>>> print(NonUniformGrid2D(nx=2, ny=2).extrude(layers=2).cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]]

>>> from fipy.meshes.tri2D import Tri2D
>>> print(Tri2D().extrude(layers=2).cellCenters.allclose([[ 0.83333333, 0.5,        0.16666667, 0.5,       0.83333333, 0.5,
...                                                      0.16666667, 0.5       ],
...                                                       [ 0.5,        0.83333333, 0.5,        0.16666667, 0.5,        0.83333333,
...                                                      0.5,        0.16666667],
...                                                      [ 0.5,        0.5,        0.5,        0.5,        1.5,        1.5,        1.5,
...                                                      1.5       ]]))
True

Parameters:

extrudeFunc (function) – Takes the vertex coordinates and returns the displaced values
layers (int) – Number of layers in the extruded mesh (number of times extrudeFunc will be called)

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property physicalShape¶: Return physical dimensions of Grid2D.

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property shape¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

fipy.meshes.uniformGrid module¶

class fipy.meshes.uniformGrid.UniformGrid(communicator, _RepresentationClass=<class 'fipy.meshes.representations.abstractRepresentation._AbstractRepresentation'>, _TopologyClass=<class 'fipy.meshes.topologies.abstractTopology._AbstractTopology'>)¶

Bases: AbstractMesh

Wrapped scaled geometry properties

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(other)¶

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(other)¶

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

fipy.meshes.uniformGrid1D module¶

1D Mesh

class fipy.meshes.uniformGrid1D.UniformGrid1D(dx=1.0, nx=1, origin=(0, ), overlap=2, communicator=SerialPETScCommWrapper(), _RepresentationClass=<class 'fipy.meshes.representations.gridRepresentation._Grid1DRepresentation'>, _TopologyClass=<class 'fipy.meshes.topologies.gridTopology._Grid1DTopology'>)¶

Bases: UniformGrid

Creates a 1D grid mesh.

>>> mesh = UniformGrid1D(nx = 3)
>>> print(mesh.cellCenters)
[[ 0.5  1.5  2.5]]

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(other)¶

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶: Geometry set and calc

property faceCellIDs¶

property faceCenters¶

property faceNormals¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property vertexCoords¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

fipy.meshes.uniformGrid2D module¶

2D rectangular Mesh with constant spacing in x and constant spacing in y

class fipy.meshes.uniformGrid2D.UniformGrid2D(dx=1.0, dy=1.0, nx=1, ny=1, origin=((0, ), (0, )), overlap=2, communicator=SerialPETScCommWrapper(), _RepresentationClass=<class 'fipy.meshes.representations.gridRepresentation._Grid2DRepresentation'>, _TopologyClass=<class 'fipy.meshes.topologies.gridTopology._Grid2DTopology'>)¶

Bases: UniformGrid

Creates a 2D grid mesh with horizontal faces numbered first and then vertical faces.

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(other)¶

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

property faceCellIDs¶

property faceCenters¶

property faceNormals¶

property faceVertexIDs¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property vertexCoords¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

fipy.meshes.uniformGrid3D module¶

class fipy.meshes.uniformGrid3D.UniformGrid3D(dx=1.0, dy=1.0, dz=1.0, nx=1, ny=1, nz=1, origin=[[0], [0], [0]], overlap=2, communicator=SerialPETScCommWrapper(), _RepresentationClass=<class 'fipy.meshes.representations.gridRepresentation._Grid3DRepresentation'>, _TopologyClass=<class 'fipy.meshes.topologies.gridTopology._Grid3DTopology'>)¶

Bases: UniformGrid

3D rectangular-prism Mesh with uniform grid spacing in each dimension.

X axis runs from left to right. Y axis runs from bottom to top. Z axis runs from front to back.

Numbering System:

Vertices: Numbered in the usual way. X coordinate changes most quickly, then Y, then Z.

* arrays are arranged Z, Y, X because in numerix, the final index is the one that changes the most quickly *

Cells: Same numbering system as vertices.

Faces: XY faces numbered first, then XZ faces, then YZ faces. Within each subcategory, it is numbered in the usual way.

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(other)¶

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

property faceCellIDs¶

property faceCenters¶

property faceNormals¶

property faceVertexIDs¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property vertexCoords¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

Module contents¶

fipy.meshes.CylindricalGrid1D(dr=None, nr=None, Lr=None, dx=1.0, nx=None, Lx=None, origin=(0,), overlap=2, communicator=SerialPETScCommWrapper())¶

Create a 2D cylindrical mesh

Factory function to select between CylindricalUniformGrid1D and CylindricalNonUniformGrid1D. If Lr is specified the length of the domain is always Lr regardless of dr, unless dr is a list of spacings, in which case Lr will be the sum of dr.

Parameters:

dr (float) – Grid spacing in the radial direction. Alternative: dx.
nr (int) – Number of cells in the radial direction. Alternative: nx.
Lr (float) – Domain length in the radial direction. Alternative: Lx.
overlap (int) – the number of overlapping cells for parallel simulations. Generally 2 is adequate. Higher order equations or discretizations require more.
communicator (CommWrapper) – MPI communicator to use. Select serialComm to create a serial mesh when running in parallel; mostly used for test purposes. (default: parallelComm).

fipy.meshes.CylindricalGrid2D(dr=None, dz=None, nr=None, nz=None, Lr=None, Lz=None, dx=1.0, dy=1.0, nx=None, ny=None, Lx=None, Ly=None, origin=((0,), (0,)), overlap=2, communicator=SerialPETScCommWrapper())¶

Create a 2D cylindrical mesh

Factory function to select between CylindricalUniformGrid2D and CylindricalNonUniformGrid2D. If Lr is specified the length of the domain is always Lr regardless of dr, unless dr is a list of spacings, in which case Lr will be the sum of dr.

Parameters:

dr (float) – Grid spacing in the radial direction. Alternative: dx.
dz (float) – grid spacing in the vertical direction. Alternative: dy.
nr (int) – Number of cells in the radial direction. Alternative: nx.
nz (int) – Number of cells in the vertical direction. Alternative: ny.
Lr (float) – Domain length in the radial direction. Alternative: Lx.
Lz (float) – Domain length in the vertical direction. Alternative: Ly.
overlap (int) – the number of overlapping cells for parallel simulations. Generally 2 is adequate. Higher order equations or discretizations require more.
communicator (CommWrapper) – MPI communicator to use. Select serialComm to create a serial mesh when running in parallel; mostly used for test purposes. (default: parallelComm).

class fipy.meshes.Gmsh2D(arg, coordDimensions=2, communicator=SerialPETScCommWrapper(), overlap=1, background=None)¶

Bases: Mesh2D

Construct a 2D Mesh using Gmsh

If called in parallel, the mesh will be partitioned based on the value of parallelComm.Nproc. If an MSH file is supplied, it must have been previously partitioned with the number of partitions matching parallelComm.Nproc.

>>> radius = 5.
>>> side = 4.
>>> squaredCircle = Gmsh2D('''
... // A mesh consisting of a square inside a circle inside a circle
...
... // define the basic dimensions of the mesh
...
... cellSize = 1;
... radius = %(radius)g;
... side = %(side)g;
...
... // define the compass points of the inner circle
...
... Point(1) = {0, 0, 0, cellSize};
... Point(2) = {-radius, 0, 0, cellSize};
... Point(3) = {0, radius, 0, cellSize};
... Point(4) = {radius, 0, 0, cellSize};
... Point(5) = {0, -radius, 0, cellSize};
...
... // define the compass points of the outer circle
...
... Point(6) = {-2*radius, 0, 0, cellSize};
... Point(7) = {0, 2*radius, 0, cellSize};
... Point(8) = {2*radius, 0, 0, cellSize};
... Point(9) = {0, -2*radius, 0, cellSize};
...
... // define the corners of the square
...
... Point(10) = {side/2, side/2, 0, cellSize/2};
... Point(11) = {-side/2, side/2, 0, cellSize/2};
... Point(12) = {-side/2, -side/2, 0, cellSize/2};
... Point(13) = {side/2, -side/2, 0, cellSize/2};
...
... // define the inner circle
...
... Circle(1) = {2, 1, 3};
... Circle(2) = {3, 1, 4};
... Circle(3) = {4, 1, 5};
... Circle(4) = {5, 1, 2};
...
... // define the outer circle
...
... Circle(5) = {6, 1, 7};
... Circle(6) = {7, 1, 8};
... Circle(7) = {8, 1, 9};
... Circle(8) = {9, 1, 6};
...
... // define the square
...
... Line(9) = {10, 13};
... Line(10) = {13, 12};
... Line(11) = {12, 11};
... Line(12) = {11, 10};
...
... // define the three boundaries
...
... Line Loop(1) = {1, 2, 3, 4};
... Line Loop(2) = {5, 6, 7, 8};
... Line Loop(3) = {9, 10, 11, 12};
...
... // define the three domains
...
... Plane Surface(1) = {2, 1};
... Plane Surface(2) = {1, 3};
... Plane Surface(3) = {3};
...
... // label the three domains
...
... // attention: if you use any "Physical" labels, you *must* label
... // all elements that correspond to FiPy Cells (Physical Surface in 2D
... // and Physical Volume in 3D) or Gmsh will not include them and FiPy
... // will not be able to include them in the Mesh.
...
... // note: if you do not use any labels, all Cells will be included.
...
... Physical Surface("Outer") = {1};
... Physical Surface("Middle") = {2};
... Physical Surface("Inner") = {3};
...
... // label the "north-west" part of the exterior boundary
...
... // note: you only need to label the Face elements
... // (Physical Line in 2D and Physical Surface in 3D) that correspond
... // to boundaries you are interested in. FiPy does not need them to
... // construct the Mesh.
...
... Physical Line("NW") = {5};
... ''' % locals()) 

It can be easier to specify certain domains and boundaries within Gmsh than it is to define the same domains and boundaries with FiPy expressions.

Here we compare obtaining the same Cells and Faces using FiPy’s parametric descriptions and Gmsh’s labels.

>>> x, y = squaredCircle.cellCenters 

>>> middle = ((x**2 + y**2 <= radius**2)
...           & ~((x > -side/2) & (x < side/2)
...               & (y > -side/2) & (y < side/2))) 

>>> print((middle == squaredCircle.physicalCells["Middle"]).all()) 
True

>>> X, Y = squaredCircle.faceCenters 

>>> NW = ((X**2 + Y**2 > (1.99*radius)**2)
...       & (X**2 + Y**2 < (2.01*radius)**2)
...       & (X <= 0) & (Y >= 0)) 

>>> print((NW == squaredCircle.physicalFaces["NW"]).all()) 
True

It is possible to direct Gmsh to give the mesh different densities in different locations

>>> geo = '''
... // A mesh consisting of a square
...
... // define the corners of the square
...
... Point(1) = {1, 1, 0, 1};
... Point(2) = {0, 1, 0, 1};
... Point(3) = {0, 0, 0, 1};
... Point(4) = {1, 0, 0, 1};
...
... // define the square
...
... Line(1) = {1, 2};
... Line(2) = {2, 3};
... Line(3) = {3, 4};
... Line(4) = {4, 1};
...
... // define the boundary
...
... Line Loop(1) = {1, 2, 3, 4};
...
... // define the domain
...
... Plane Surface(1) = {1};
... '''

>>> from fipy import CellVariable, numerix

>>> error = []
>>> bkg = None
>>> from builtins import range
>>> for refine in range(4):
...     square = Gmsh2D(geo, background=bkg) 
...     x, y = square.cellCenters 
...     bkg = CellVariable(mesh=square, value=abs(x / 4) + 0.01) 
...     error.append(((2 * numerix.sqrt(square.cellVolumes) / bkg - 1)**2).cellVolumeAverage) 

Check that the mesh is (semi)monotonically approaching the desired density (the first step may increase, depending on the number of partitions)

>>> print(numerix.greater(error[:-1], error[1:]).all()) 
True

and that the final density is close enough to the desired density

>>> print(error[-1] < 0.02) 
True

The initial mesh doesn’t have to be from Gmsh

>>> from fipy import Tri2D

>>> trisquare = Tri2D(nx=1, ny=1)
>>> x, y = trisquare.cellCenters
>>> bkg = CellVariable(mesh=trisquare, value=abs(x / 4) + 0.01)
>>> std1 = (numerix.sqrt(2 * trisquare.cellVolumes) / bkg).std()

>>> square = Gmsh2D(geo, background=bkg) 
>>> x, y = square.cellCenters 
>>> bkg = CellVariable(mesh=square, value=abs(x / 4) + 0.01) 
>>> std2 = (numerix.sqrt(2 * square.cellVolumes) / bkg).std() 

>>> print(std1 > std2) 
True

Parameters:

arg (str) – (i) the path to an MSH file, (ii) a path to a Gmsh geometry (.geo) file, or (iii) a Gmsh geometry script
coordDimensions (int) – Dimension of shapes
overlap (int) – The number of overlapping cells for parallel simulations. Generally 1 is adequate. Higher order equations or discretizations require more. If overlap is greater than one, communication reverts to serial, as Gmsh only provides one layer of ghost cells.
background (CellVariable) – Specifies the desired characteristic lengths of the mesh cells

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

extrude(extrudeFunc=<function Mesh2D.<lambda>>, layers=1)¶

This function returns a new 3D mesh. The 2D mesh is extruded using the extrudeFunc and the number of layers.

>>> from fipy.meshes.nonUniformGrid2D import NonUniformGrid2D
>>> print(NonUniformGrid2D(nx=2, ny=2).extrude(layers=2).cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]]

>>> from fipy.meshes.tri2D import Tri2D
>>> print(Tri2D().extrude(layers=2).cellCenters.allclose([[ 0.83333333, 0.5,        0.16666667, 0.5,       0.83333333, 0.5,
...                                                      0.16666667, 0.5       ],
...                                                       [ 0.5,        0.83333333, 0.5,        0.16666667, 0.5,        0.83333333,
...                                                      0.5,        0.16666667],
...                                                      [ 0.5,        0.5,        0.5,        0.5,        1.5,        1.5,        1.5,
...                                                      1.5       ]]))
True

Parameters:

extrudeFunc (function) – Takes the vertex coordinates and returns the displaced values
layers (int) – Number of layers in the extruded mesh (number of times extrudeFunc will be called)

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

class fipy.meshes.Gmsh2DIn3DSpace(arg, communicator=SerialPETScCommWrapper(), overlap=1, background=None)¶

Bases: Gmsh2D

Create a topologically 2D Mesh in 3D coordinates using Gmsh

If called in parallel, the mesh will be partitioned based on the value of parallelComm.Nproc. If an MSH file is supplied, it must have been previously partitioned with the number of partitions matching parallelComm.Nproc.

Parameters:

arg (str) – (i) the path to an MSH file, (ii) a path to a Gmsh geometry (.geo) file, or (iii) a Gmsh geometry script
coordDimensions (int) – Dimension of shapes
overlap (int) – The number of overlapping cells for parallel simulations. Generally 1 is adequate. Higher order equations or discretizations require more. If overlap is greater than one, communication reverts to serial, as Gmsh only provides one layer of ghost cells.
background (CellVariable) – Specifies the desired characteristic lengths of the mesh cells

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

extrude(extrudeFunc=<function Mesh2D.<lambda>>, layers=1)¶

This function returns a new 3D mesh. The 2D mesh is extruded using the extrudeFunc and the number of layers.

>>> from fipy.meshes.nonUniformGrid2D import NonUniformGrid2D
>>> print(NonUniformGrid2D(nx=2, ny=2).extrude(layers=2).cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]]

>>> from fipy.meshes.tri2D import Tri2D
>>> print(Tri2D().extrude(layers=2).cellCenters.allclose([[ 0.83333333, 0.5,        0.16666667, 0.5,       0.83333333, 0.5,
...                                                      0.16666667, 0.5       ],
...                                                       [ 0.5,        0.83333333, 0.5,        0.16666667, 0.5,        0.83333333,
...                                                      0.5,        0.16666667],
...                                                      [ 0.5,        0.5,        0.5,        0.5,        1.5,        1.5,        1.5,
...                                                      1.5       ]]))
True

Parameters:

extrudeFunc (function) – Takes the vertex coordinates and returns the displaced values
layers (int) – Number of layers in the extruded mesh (number of times extrudeFunc will be called)

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

class fipy.meshes.Gmsh3D(arg, communicator=SerialPETScCommWrapper(), overlap=1, background=None)¶

Bases: Mesh

Create a 3D Mesh using Gmsh

If called in parallel, the mesh will be partitioned based on the value of parallelComm.Nproc. If an MSH file is supplied, it must have been previously partitioned with the number of partitions matching parallelComm.Nproc.

Parameters:

arg (str) – (i) the path to an MSH file, (ii) a path to a Gmsh geometry (.geo) file, or (iii) a Gmsh geometry script
overlap (int) – The number of overlapping cells for parallel simulations. Generally 1 is adequate. Higher order equations or discretizations require more. If overlap is greater than one, communication reverts to serial, as Gmsh only provides one layer of ghost cells.
background (CellVariable) – Specifies the desired characteristic lengths of the mesh cells

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

class fipy.meshes.GmshGrid2D(dx=1.0, dy=1.0, nx=1, ny=None, coordDimensions=2, communicator=SerialPETScCommWrapper(), overlap=1)¶

Bases: Gmsh2D

Should serve as a drop-in replacement for Grid2D

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

extrude(extrudeFunc=<function Mesh2D.<lambda>>, layers=1)¶

This function returns a new 3D mesh. The 2D mesh is extruded using the extrudeFunc and the number of layers.

>>> from fipy.meshes.nonUniformGrid2D import NonUniformGrid2D
>>> print(NonUniformGrid2D(nx=2, ny=2).extrude(layers=2).cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]]

>>> from fipy.meshes.tri2D import Tri2D
>>> print(Tri2D().extrude(layers=2).cellCenters.allclose([[ 0.83333333, 0.5,        0.16666667, 0.5,       0.83333333, 0.5,
...                                                      0.16666667, 0.5       ],
...                                                       [ 0.5,        0.83333333, 0.5,        0.16666667, 0.5,        0.83333333,
...                                                      0.5,        0.16666667],
...                                                      [ 0.5,        0.5,        0.5,        0.5,        1.5,        1.5,        1.5,
...                                                      1.5       ]]))
True

Parameters:

extrudeFunc (function) – Takes the vertex coordinates and returns the displaced values
layers (int) – Number of layers in the extruded mesh (number of times extrudeFunc will be called)

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

class fipy.meshes.GmshGrid3D(dx=1.0, dy=1.0, dz=1.0, nx=1, ny=None, nz=None, communicator=SerialPETScCommWrapper(), overlap=1)¶

Bases: Gmsh3D

Should serve as a drop-in replacement for Grid3D

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

fipy.meshes.Grid1D(dx=1.0, nx=None, Lx=None, overlap=2, communicator=SerialPETScCommWrapper())¶

Create a 1D Cartesian mesh

Factory function to select between UniformGrid1D and NonUniformGrid1D. If Lx is specified the length of the domain is always Lx regardless of dx, unless dx is a list of spacings, in which case Lx will be the sum of dx and nx will be the count of dx.

Parameters:

dx (float) – Grid spacing in the horizontal direction
nx (int) – Number of cells in the horizontal direction
Lx (float) – Domain length in the horizontal direction
overlap (int) – Number of overlapping cells for parallel simulations. Generally 2 is adequate. Higher order equations or discretizations require more.
communicator (CommWrapper) – MPI communicator to use. Select serialComm to create a serial mesh when running in parallel; mostly used for test purposes. (default: parallelComm).

fipy.meshes.Grid2D(dx=1.0, dy=1.0, nx=None, ny=None, Lx=None, Ly=None, overlap=2, communicator=SerialPETScCommWrapper())¶

Create a 2D Cartesian mesh

Factory function to select between UniformGrid2D and NonUniformGrid2D. If L{x,y} is specified, the length of the domain is always L{x,y} regardless of d{x,y}, unless d{x,y} is a list of spacings, in which case L{x,y} will be the sum of d{x,y} and n{x,y} will be the count of d{x,y}.

>>> print(Grid2D(Lx=3., nx=2).dx)
1.5

Parameters:

dx (float) – Grid spacing in the horizontal direction
dy (float) – Grid spacing in the vertical direction
nx (int) – Number of cells in the horizontal direction
ny (int) – Number of cells in the vertical direction
Lx (float) – Domain length in the horizontal direction
Ly (float) – Domain length in the vertical direction
overlap (int) – Number of overlapping cells for parallel simulations. Generally 2 is adequate. Higher order equations or discretizations require more.
communicator (CommWrapper) – MPI communicator to use. Select serialComm to create a serial mesh when running in parallel; mostly used for test purposes. (default: parallelComm).

fipy.meshes.Grid3D(dx=1.0, dy=1.0, dz=1.0, nx=None, ny=None, nz=None, Lx=None, Ly=None, Lz=None, overlap=2, communicator=SerialPETScCommWrapper())¶

Create a 3D Cartesian mesh

Factory function to select between UniformGrid3D and NonUniformGrid3D. If L{x,y,z} is specified, the length of the domain is always L{x,y,z} regardless of d{x,y,z}, unless d{x,y,z} is a list of spacings, in which case L{x,y,z} will be the sum of d{x,y,z} and n{x,y,z} will be the count of d{x,y,z}.

Parameters:

dx (float) – Grid spacing in the horizontal direction
dy (float) – Grid spacing in the vertical direction
dz (float) – Grid spacing in the depth direction
nx (int) – Number of cells in the horizontal direction
ny (int) – Number of cells in the vertical direction
nz (int) – Number of cells in the depth direction
Lx (float) – Domain length in the horizontal direction
Ly (float) – Domain length in the vertical direction
Lz (float) – Domain length in the depth direction
overlap (int) – Number of overlapping cells for parallel simulations. Generally 2 is adequate. Higher order equations or discretizations require more.
communicator (CommWrapper) – MPI communicator to use. Select serialComm to create a serial mesh when running in parallel; mostly used for test purposes. (default: parallelComm).

class fipy.meshes.PeriodicGrid1D(dx=1.0, nx=None, overlap=2, *args, **kwargs)¶

Bases: NonUniformGrid1D

Creates a Periodic grid mesh.

>>> mesh = PeriodicGrid1D(dx = (1, 2, 3))

>>> print(numerix.allclose(numerix.nonzero(mesh.exteriorFaces)[0],
...                        [3])) 
True

>>> print(numerix.allclose(mesh.faceCellIDs.filled(-999),
...                        [[2, 0, 1, 2],
...                         [0, 1, 2, -999]])) 
True

>>> print(numerix.allclose(mesh._cellDistances,
...                        [ 2., 1.5, 2.5, 1.5])) 
True

>>> print(numerix.allclose(mesh._cellToCellDistances,
...                        [[ 2.,   1.5,  2.5],
...                         [ 1.5,  2.5,  2. ]])) 
True

>>> print(numerix.allclose(mesh.faceNormals,
...                        [[ 1.,  1.,  1.,  1.]])) 
True

>>> print(numerix.allclose(mesh._cellVertexIDs,
...                        [[1, 2, 2],
...                        [0, 1, 0]])) 
True

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶: Defined outside of a geometry class since we need the CellVariable version of cellCenters; that is, the cellCenters defined in fipy.meshes.mesh and not in any geometry (since a CellVariable requires a reference to a mesh).

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

class fipy.meshes.PeriodicGrid2D(dx=1.0, dy=1.0, nx=None, ny=None, overlap=2, communicator=SerialPETScCommWrapper(), *args, **kwargs)¶

Bases: _BasePeriodicGrid2D

Creates a periodic 2D grid mesh with horizontal faces numbered first and then vertical faces. Vertices and cells are numbered in the usual way.

>>> from fipy import numerix

>>> mesh = PeriodicGrid2D(dx = 1., dy = 0.5, nx = 2, ny = 2)

>>> print(numerix.allclose(numerix.nonzero(mesh.exteriorFaces)[0],
...                        [ 4,  5,  8, 11]))  
True

>>> print(numerix.allclose(mesh.faceCellIDs.filled(-1),
...                        [[2, 3, 0, 1, 2, 3, 1, 0, 1, 3, 2, 3],
...                         [0, 1, 2, 3, -1, -1, 0, 1, -1, 2, 3, -1]])) 
True

>>> print(numerix.allclose(mesh._cellDistances,
...                        [ 0.5, 0.5, 0.5, 0.5, 0.25, 0.25, 1., 1., 0.5, 1., 1., 0.5])) 
True

>>> print(numerix.allclose(mesh.cellFaceIDs,
...                        [[0, 1, 2, 3],
...                         [7, 6, 10, 9],
...                         [2, 3, 0, 1],
...                         [6, 7, 9, 10]])) 
True

>>> print(numerix.allclose(mesh._cellToCellDistances,
...                        [[ 0.5, 0.5, 0.5, 0.5],
...                         [ 1., 1., 1., 1. ],
...                         [ 0.5, 0.5, 0.5, 0.5],
...                         [ 1., 1., 1., 1. ]])) 
True

>>> normals = [[0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1],
...            [1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0]]

>>> print(numerix.allclose(mesh.faceNormals, normals)) 
True

>>> print(numerix.allclose(mesh._cellVertexIDs,
...                        [[4, 5, 7, 8],
...                         [3, 4, 6, 7],
...                         [1, 2, 4, 5],
...                         [0, 1, 3, 4]])) 
True

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

extrude(extrudeFunc=<function Mesh2D.<lambda>>, layers=1)¶

This function returns a new 3D mesh. The 2D mesh is extruded using the extrudeFunc and the number of layers.

>>> from fipy.meshes.nonUniformGrid2D import NonUniformGrid2D
>>> print(NonUniformGrid2D(nx=2, ny=2).extrude(layers=2).cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]]

>>> from fipy.meshes.tri2D import Tri2D
>>> print(Tri2D().extrude(layers=2).cellCenters.allclose([[ 0.83333333, 0.5,        0.16666667, 0.5,       0.83333333, 0.5,
...                                                      0.16666667, 0.5       ],
...                                                       [ 0.5,        0.83333333, 0.5,        0.16666667, 0.5,        0.83333333,
...                                                      0.5,        0.16666667],
...                                                      [ 0.5,        0.5,        0.5,        0.5,        1.5,        1.5,        1.5,
...                                                      1.5       ]]))
True

Parameters:

extrudeFunc (function) – Takes the vertex coordinates and returns the displaced values
layers (int) – Number of layers in the extruded mesh (number of times extrudeFunc will be called)

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

class fipy.meshes.PeriodicGrid2DLeftRight(dx=1.0, dy=1.0, nx=None, ny=None, overlap=2, communicator=SerialPETScCommWrapper(), *args, **kwargs)¶

Bases: _BasePeriodicGrid2D

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

extrude(extrudeFunc=<function Mesh2D.<lambda>>, layers=1)¶

This function returns a new 3D mesh. The 2D mesh is extruded using the extrudeFunc and the number of layers.

>>> from fipy.meshes.nonUniformGrid2D import NonUniformGrid2D
>>> print(NonUniformGrid2D(nx=2, ny=2).extrude(layers=2).cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]]

>>> from fipy.meshes.tri2D import Tri2D
>>> print(Tri2D().extrude(layers=2).cellCenters.allclose([[ 0.83333333, 0.5,        0.16666667, 0.5,       0.83333333, 0.5,
...                                                      0.16666667, 0.5       ],
...                                                       [ 0.5,        0.83333333, 0.5,        0.16666667, 0.5,        0.83333333,
...                                                      0.5,        0.16666667],
...                                                      [ 0.5,        0.5,        0.5,        0.5,        1.5,        1.5,        1.5,
...                                                      1.5       ]]))
True

Parameters:

extrudeFunc (function) – Takes the vertex coordinates and returns the displaced values
layers (int) – Number of layers in the extruded mesh (number of times extrudeFunc will be called)

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

class fipy.meshes.PeriodicGrid2DTopBottom(dx=1.0, dy=1.0, nx=None, ny=None, overlap=2, communicator=SerialPETScCommWrapper(), *args, **kwargs)¶

Bases: _BasePeriodicGrid2D

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

extrude(extrudeFunc=<function Mesh2D.<lambda>>, layers=1)¶

This function returns a new 3D mesh. The 2D mesh is extruded using the extrudeFunc and the number of layers.

>>> from fipy.meshes.nonUniformGrid2D import NonUniformGrid2D
>>> print(NonUniformGrid2D(nx=2, ny=2).extrude(layers=2).cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]]

>>> from fipy.meshes.tri2D import Tri2D
>>> print(Tri2D().extrude(layers=2).cellCenters.allclose([[ 0.83333333, 0.5,        0.16666667, 0.5,       0.83333333, 0.5,
...                                                      0.16666667, 0.5       ],
...                                                       [ 0.5,        0.83333333, 0.5,        0.16666667, 0.5,        0.83333333,
...                                                      0.5,        0.16666667],
...                                                      [ 0.5,        0.5,        0.5,        0.5,        1.5,        1.5,        1.5,
...                                                      1.5       ]]))
True

Parameters:

extrudeFunc (function) – Takes the vertex coordinates and returns the displaced values
layers (int) – Number of layers in the extruded mesh (number of times extrudeFunc will be called)

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

class fipy.meshes.PeriodicGrid3D(dx=1.0, dy=1.0, dz=1.0, nx=None, ny=None, nz=None, overlap=2, communicator=SerialPETScCommWrapper(), *args, **kwargs)¶

Bases: _BasePeriodicGrid3D

Creates a periodic 3D grid mesh with horizontal faces numbered first and then vertical faces. Vertices and cells are numbered in the usual way.

>>> from fipy import numerix

>>> mesh = PeriodicGrid3D(dx=1., dy=0.5, dz=2., nx=2, ny=2, nz=1)
>>> print(numerix.allclose(numerix.nonzero(mesh.exteriorFaces)[0],
...                        [4, 5, 6, 7, 12, 13, 16, 19]))  
True

>>> print(numerix.allclose(mesh.faceCellIDs.filled(-1),
...                        [[0, 1, 2, 3, 0, 1, 2, 3, 2, 3,
...                          0, 1, 2, 3, 1, 0, 1, 3, 2, 3],
...                         [0, 1, 2, 3, -1, -1, -1, -1, 0, 1,
...                          2, 3, -1, -1, 0, 1, -1, 2, 3, -1]])) 
True

>>> print(numerix.allclose(mesh._cellDistances,
...                        [2., 2., 2., 2., 1., 1., 1., 1., 0.5, 0.5,
...                         0.5, 0.5, 0.25, 0.25, 1., 1., 0.5, 1., 1., 0.5])) 
True

>>> print(numerix.allclose(mesh.cellFaceIDs,
...                        [[14, 15, 17, 18],
...                         [15, 14, 18, 17],
...                         [8, 9, 10, 11],
...                         [10, 11, 8, 9],
...                         [0, 1, 2, 3],
...                         [0, 1, 2, 3]])) 
True

>>> print(numerix.allclose(mesh._cellToCellDistances,
...                        [[1., 1., 1., 1.],
...                         [1., 1., 1., 1.],
...                         [0.5, 0.5, 0.5, 0.5],
...                         [0.5, 0.5, 0.5, 0.5],
...                         [2., 2., 2., 2.],
...                         [2., 2., 2., 2.]])) 
True

>>> normals = [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1],
...            [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0],
...            [1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]

>>> print(numerix.allclose(mesh.faceNormals, normals)) 
True

>>> print(numerix.allclose(mesh._cellVertexIDs,
...                        [[13, 14, 16, 17],
...                         [12, 13, 15, 16],
...                         [10, 11, 13, 14],
...                         [9, 10, 12, 13],
...                         [4, 5, 7, 8],
...                         [3, 4, 6, 7],
...                         [1, 2, 4, 5],
...                         [0, 1, 3, 4]])) 
True

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

class fipy.meshes.PeriodicGrid3DFrontBack(dx=1.0, dy=1.0, dz=1.0, nx=None, ny=None, nz=None, overlap=2, communicator=SerialPETScCommWrapper(), *args, **kwargs)¶

Bases: _BasePeriodicGrid3D

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

class fipy.meshes.PeriodicGrid3DLeftRight(dx=1.0, dy=1.0, dz=1.0, nx=None, ny=None, nz=None, overlap=2, communicator=SerialPETScCommWrapper(), *args, **kwargs)¶

Bases: _BasePeriodicGrid3D

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

class fipy.meshes.PeriodicGrid3DLeftRightFrontBack(dx=1.0, dy=1.0, dz=1.0, nx=None, ny=None, nz=None, overlap=2, communicator=SerialPETScCommWrapper(), *args, **kwargs)¶

Bases: _BasePeriodicGrid3D

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

class fipy.meshes.PeriodicGrid3DLeftRightTopBottom(dx=1.0, dy=1.0, dz=1.0, nx=None, ny=None, nz=None, overlap=2, communicator=SerialPETScCommWrapper(), *args, **kwargs)¶

Bases: _BasePeriodicGrid3D

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

class fipy.meshes.PeriodicGrid3DTopBottom(dx=1.0, dy=1.0, dz=1.0, nx=None, ny=None, nz=None, overlap=2, communicator=SerialPETScCommWrapper(), *args, **kwargs)¶

Bases: _BasePeriodicGrid3D

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

class fipy.meshes.PeriodicGrid3DTopBottomFrontBack(dx=1.0, dy=1.0, dz=1.0, nx=None, ny=None, nz=None, overlap=2, communicator=SerialPETScCommWrapper(), *args, **kwargs)¶

Bases: _BasePeriodicGrid3D

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

class fipy.meshes.SkewedGrid2D(dx=1.0, dy=1.0, nx=None, ny=1, rand=0, *args, **kwargs)¶

Bases: Mesh2D

Creates a 2D grid mesh with horizontal faces numbered first and then vertical faces. The points are skewed by a random amount (between rand and -rand) in the X and Y directions.

Note

This Mesh only operates in serial

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

extrude(extrudeFunc=<function Mesh2D.<lambda>>, layers=1)¶

This function returns a new 3D mesh. The 2D mesh is extruded using the extrudeFunc and the number of layers.

>>> from fipy.meshes.nonUniformGrid2D import NonUniformGrid2D
>>> print(NonUniformGrid2D(nx=2, ny=2).extrude(layers=2).cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]]

>>> from fipy.meshes.tri2D import Tri2D
>>> print(Tri2D().extrude(layers=2).cellCenters.allclose([[ 0.83333333, 0.5,        0.16666667, 0.5,       0.83333333, 0.5,
...                                                      0.16666667, 0.5       ],
...                                                       [ 0.5,        0.83333333, 0.5,        0.16666667, 0.5,        0.83333333,
...                                                      0.5,        0.16666667],
...                                                      [ 0.5,        0.5,        0.5,        0.5,        1.5,        1.5,        1.5,
...                                                      1.5       ]]))
True

Parameters:

extrudeFunc (function) – Takes the vertex coordinates and returns the displaced values
layers (int) – Number of layers in the extruded mesh (number of times extrudeFunc will be called)

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property physicalShape¶: Return physical dimensions of Grid2D.

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property shape¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

fipy.meshes.SphericalGrid1D(dr=None, nr=None, Lr=None, dx=1.0, nx=None, Lx=None, origin=(0,), overlap=2, communicator=SerialPETScCommWrapper())¶

Create a 1D spherical mesh

Factory function to select between SphericalUniformGrid1D and SphericalNonUniformGrid1D. If Lr is specified the length of the domain is always Lr regardless of dr, unless dr is a list of spacings, in which case Lr will be the sum of dr.

Parameters:

dr (float) – Grid spacing in the radial direction. Alternative: dx.
nr (int) – Number of cells in the radial direction. Alternative: nx.
Lr (float) – Domain length in the radial direction. Alternative: Lx.
overlap (int) – the number of overlapping cells for parallel simulations. Generally 2 is adequate. Higher order equations or discretizations require more.
communicator (CommWrapper) – MPI communicator to use. Select serialComm to create a serial mesh when running in parallel; mostly used for test purposes. (default: parallelComm).

class fipy.meshes.Tri2D(dx=1.0, dy=1.0, nx=1, ny=1, _RepresentationClass=<class 'fipy.meshes.representations.gridRepresentation._Grid2DRepresentation'>, _TopologyClass=<class 'fipy.meshes.topologies.meshTopology._Mesh2DTopology'>)¶

Bases: Mesh2D

This class creates a mesh made out of triangles. It does this by starting with a standard Cartesian mesh (Grid2D) and dividing each cell in that mesh (hereafter referred to as a “box”) into four equal parts with the dividing lines being the diagonals.

Creates a 2D triangular mesh with horizontal faces numbered first then vertical faces, then diagonal faces. Vertices are numbered starting with the vertices at the corners of boxes and then the vertices at the centers of boxes. Cells on the right of boxes are numbered first, then cells on the top of boxes, then cells on the left of boxes, then cells on the bottom of boxes. Within each of the “sub-categories” in the above, the vertices, cells and faces are numbered in the usual way.

Parameters:

dx (float) – The X and Y dimensions of each “box”. If dx <> dy, the line segments connecting the cell centers will not be orthogonal to the faces.
dy (float) – The X and Y dimensions of each “box”. If dx <> dy, the line segments connecting the cell centers will not be orthogonal to the faces.
nx (int) – The number of boxes in the X direction and the Y direction. The total number of boxes will be equal to nx * ny, and the total number of cells will be equal to 4 * nx * ny.
ny (int) – The number of boxes in the X direction and the Y direction. The total number of boxes will be equal to nx * ny, and the total number of cells will be equal to 4 * nx * ny.

property VTKCellDataSet¶: Returns a TVTK DataSet representing the cells of this mesh

property VTKFaceDataSet¶: Returns a TVTK DataSet representing the face centers of this mesh

__add__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__div__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

__getstate__()¶: Helper for pickle.

__mul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__radd__(other)¶

Either translate a Mesh or concatenate two Mesh objects.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

If a vector is added to a Mesh, a translated Mesh is returned

>>> translatedMesh = baseMesh + ((5,), (10,))
>>> print(translatedMesh.cellCenters)
[[  5.5   6.5   5.5   6.5]
 [ 10.5  10.5  11.5  11.5]]

If a Mesh is added to a Mesh, a concatenation of the two Mesh objects is returned

>>> addedMesh = baseMesh + (baseMesh + ((2,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

The two Mesh objects need not be properly aligned in order to concatenate them but the resulting mesh may not have the intended connectivity

>>> addedMesh = baseMesh + (baseMesh + ((3,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  3.5  4.5  3.5  4.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

>>> addedMesh = baseMesh + (baseMesh + ((2,), (2,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  2.5  3.5  2.5  3.5]
 [ 0.5  0.5  1.5  1.5  2.5  2.5  3.5  3.5]]

No provision is made to avoid or consolidate overlapping Mesh objects

>>> addedMesh = baseMesh + (baseMesh + ((1,), (0,)))
>>> print(addedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  1.5  2.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]]

Different Mesh classes can be concatenated

>>> from fipy.meshes import Tri2D
>>> triMesh = Tri2D(dx = 1.0, dy = 1.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[0.5, 1.5, 0.5, 1.5, 2.83333333,  3.83333333,
...                 2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [0.5, 0.5, 1.5, 1.5, 0.5, 0.5, 0.83333333, 0.83333333,
...                 0.5, 0.5, 0.16666667, 0.16666667]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

again, their faces need not align, but the mesh may not have the desired connectivity

>>> triMesh = Tri2D(dx = 1.0, dy = 2.0, nx = 2, ny = 1)
>>> triMesh = triMesh + ((2,), (0,))
>>> triAddedMesh = baseMesh + triMesh
>>> cellCenters = [[ 0.5, 1.5, 0.5, 1.5, 2.83333333, 3.83333333,
...                  2.5, 3.5, 2.16666667, 3.16666667, 2.5, 3.5],
...                [ 0.5, 0.5, 1.5, 1.5, 1., 1.,
...                  1.66666667, 1.66666667, 1., 1., 0.33333333, 0.33333333]]
>>> print(numerix.allclose(triAddedMesh.cellCenters,
...                        cellCenters))
True

Mesh concatenation is not limited to 2D meshes

>>> from fipy.meshes import Grid3D
>>> threeDBaseMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                         nx = 2, ny = 2, nz = 2)
>>> threeDSecondMesh = Grid3D(dx = 1.0, dy = 1.0, dz = 1.0,
...                           nx = 1, ny = 1, nz = 1)
>>> threeDAddedMesh = threeDBaseMesh + (threeDSecondMesh + ((2,), (0,), (0,)))
>>> print(threeDAddedMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  2.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5  0.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5  0.5]]

but the different Mesh objects must, of course, have the same dimensionality.

>>> InvalidMesh = threeDBaseMesh + baseMesh 
Traceback (most recent call last):
...
MeshAdditionError: Dimensions do not match

__repr__()¶: Return repr(self).

__rmul__(factor)¶

Dilate a Mesh by factor.

>>> from fipy.meshes import Grid2D
>>> baseMesh = Grid2D(dx = 1.0, dy = 1.0, nx = 2, ny = 2)
>>> print(baseMesh.cellCenters)
[[ 0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5]]

The factor can be a scalar

>>> dilatedMesh = baseMesh * 3
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.5  1.5  4.5  4.5]]

or a vector

>>> dilatedMesh = baseMesh * ((3,), (2,))
>>> print(dilatedMesh.cellCenters)
[[ 1.5  4.5  1.5  4.5]
 [ 1.   1.   3.   3. ]]

but the vector must have the same dimensionality as the Mesh

>>> dilatedMesh = baseMesh * ((3,), (2,), (1,)) 
Traceback (most recent call last):
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape

__setstate__(state)¶

__sub__(other)¶: Tests. >>> from fipy import * >>> m = Grid1D() >>> print((m - ((1,))).cellCenters) [[-0.5]] >>> ((1,)) - m Traceback (most recent call last): … TypeError: unsupported operand type(s) for -: ‘tuple’ and ‘UniformGrid1D’

__truediv__(other)¶: Tests. >>> from fipy import * >>> print((Grid1D(nx=1) / 2.).cellCenters) [[ 0.25]] >>> AbstractMesh(communicator=None) / 2. Traceback (most recent call last): … NotImplementedError

property aspect2D¶: The physical y vs x aspect ratio of a 2D mesh

property cellCenters¶

property cellDistanceVectors¶

property cellFaceIDs¶

property cellToFaceDistanceVectors¶

property cellVolumes¶

property extents¶

property exteriorFaces¶

extrude(extrudeFunc=<function Mesh2D.<lambda>>, layers=1)¶

This function returns a new 3D mesh. The 2D mesh is extruded using the extrudeFunc and the number of layers.

>>> from fipy.meshes.nonUniformGrid2D import NonUniformGrid2D
>>> print(NonUniformGrid2D(nx=2, ny=2).extrude(layers=2).cellCenters)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5]
 [ 0.5  0.5  1.5  1.5  0.5  0.5  1.5  1.5]
 [ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]]

>>> from fipy.meshes.tri2D import Tri2D
>>> print(Tri2D().extrude(layers=2).cellCenters.allclose([[ 0.83333333, 0.5,        0.16666667, 0.5,       0.83333333, 0.5,
...                                                      0.16666667, 0.5       ],
...                                                       [ 0.5,        0.83333333, 0.5,        0.16666667, 0.5,        0.83333333,
...                                                      0.5,        0.16666667],
...                                                      [ 0.5,        0.5,        0.5,        0.5,        1.5,        1.5,        1.5,
...                                                      1.5       ]]))
True

Parameters:

extrudeFunc (function) – Takes the vertex coordinates and returns the displaced values
layers (int) – Number of layers in the extruded mesh (number of times extrudeFunc will be called)

property faceCenters¶

property facesBack¶

Return list of faces on back boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((6, 7, 8, 9, 10, 11),
...                        numerix.nonzero(mesh.facesBack)[0])) 
True
>>> ignore = mesh.facesBack.value 

property facesBottom¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesDown¶

Return list of faces on bottom boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((12, 13, 14),
...                        numerix.nonzero(mesh.facesBottom)[0])) 
True
>>> ignore = mesh.facesBottom.value 
>>> x, y, z = mesh.faceCenters
>>> print(numerix.allequal((12, 13),
...                        numerix.nonzero(mesh.facesBottom & (x < 1))[0])) 
True
>>> ignore = mesh.facesBottom.value 

property facesFront¶

Return list of faces on front boundary of 3D Mesh with the z-axis running from front to back.

>>> from fipy import Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((0, 1, 2, 3, 4, 5),
...                        numerix.nonzero(mesh.facesFront)[0])) 
True
>>> ignore = mesh.facesFront.value 

property facesLeft¶

Return face on left boundary of Mesh as list with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((21, 25),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((9, 13),
...                        numerix.nonzero(mesh.facesLeft)[0])) 
True
>>> ignore = mesh.facesLeft.value 

property facesRight¶

Return list of faces on right boundary of Mesh with the x-axis running from left to right.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((24, 28),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((12, 16),
...                        numerix.nonzero(mesh.facesRight)[0])) 
True
>>> ignore = mesh.facesRight.value 

property facesTop¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

property facesUp¶

Return list of faces on top boundary of 2D or 3D Mesh with the y-axis running from bottom to top.

>>> from fipy import Grid2D, Grid3D, numerix
>>> mesh = Grid3D(nx = 3, ny = 2, nz = 1, dx = 0.5, dy = 2., dz = 4.)
>>> print(numerix.allequal((18, 19, 20),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 
>>> mesh = Grid2D(nx = 3, ny = 2, dx = 0.5, dy = 2.)
>>> print(numerix.allequal((6, 7, 8),
...                        numerix.nonzero(mesh.facesTop)[0])) 
True
>>> ignore = mesh.facesTop.value 

getNearestCell(point)¶

property interiorFaceCellIDs¶

property interiorFaceIDs¶

property interiorFaces¶

property physicalShape¶: Return physical dimensions of Grid2D.

property scale¶

property scaledCellDistances¶

property scaledCellToCellDistances¶

property scaledCellVolumes¶

property scaledFaceAreas¶

property scaledFaceToCellDistances¶

property shape¶

property x¶

Equivalent to using cellCenters[0].

>>> from fipy import *
>>> print(Grid1D(nx=2).x)
[ 0.5  1.5]

property y¶

Equivalent to using cellCenters[1].

>>> from fipy import *
>>> print(Grid2D(nx=2, ny=2).y)
[ 0.5  0.5  1.5  1.5]
>>> print(Grid1D(nx=2).y)
Traceback (most recent call last):
  ...
AttributeError: 1D meshes do not have a "y" attribute.

property z¶

Equivalent to using cellCenters[2].

>>> from fipy import *
>>> print(Grid3D(nx=2, ny=2, nz=2).z)
[ 0.5  0.5  0.5  0.5  1.5  1.5  1.5  1.5]
>>> print(Grid2D(nx=2, ny=2).z)
Traceback (most recent call last):
  ...
AttributeError: 1D and 2D meshes do not have a "z" attribute.

fipy.meshes.openMSHFile(name, dimensions=None, coordDimensions=None, communicator=SerialPETScCommWrapper(), overlap=1, mode='r', background=None)¶

Open a Gmsh MSH file

Parameters:

filename (str) – Gmsh output file
dimensions (int) – Dimension of mesh
coordDimensions (int) – Dimension of shapes
overlap (int) – The number of overlapping cells for parallel simulations. Generally 1 is adequate. Higher order equations or discretizations require more. If overlap is greater than one, communication reverts to serial, as Gmsh only provides one layer of ghost cells.
mode (str) – Beginning with r for reading and w for writing. The file will be created if it doesn’t exist when opened for writing; it will be truncated when opened for writing. Add a b to the mode for binary files.
background (CellVariable) – Specifies the desired characteristic lengths of the mesh cells

fipy.meshes.openPOSFile(name, communicator=SerialPETScCommWrapper(), mode='w')¶: Open a Gmsh POS post-processing file

Last updated on Jun 27, 2023. Created using Sphinx 6.2.1.

fipy.meshes package¶

Subpackages¶

Submodules¶

fipy.meshes.abstractMesh module¶

fipy.meshes.cylindricalGrid1D module¶

fipy.meshes.cylindricalGrid2D module¶

fipy.meshes.cylindricalNonUniformGrid1D module¶

fipy.meshes.cylindricalNonUniformGrid2D module¶

fipy.meshes.cylindricalUniformGrid1D module¶

fipy.meshes.cylindricalUniformGrid2D module¶

fipy.meshes.factoryMeshes module¶

fipy.meshes.gmshMesh module¶

fipy.meshes.grid1D module¶

fipy.meshes.grid2D module¶

fipy.meshes.grid3D module¶

fipy.meshes.mesh module¶

fipy.meshes.mesh1D module¶

fipy.meshes.mesh2D module¶

fipy.meshes.nonUniformGrid1D module¶

fipy.meshes.nonUniformGrid2D module¶

fipy.meshes.nonUniformGrid3D module¶

fipy.meshes.periodicGrid1D module¶

fipy.meshes.periodicGrid2D module¶

fipy.meshes.periodicGrid3D module¶

fipy.meshes.skewedGrid2D module¶

fipy.meshes.sphericalNonUniformGrid1D module¶

fipy.meshes.sphericalUniformGrid1D module¶

fipy.meshes.test module¶

fipy.meshes.tri2D module¶

fipy.meshes.uniformGrid module¶

fipy.meshes.uniformGrid1D module¶

fipy.meshes.uniformGrid2D module¶

fipy.meshes.uniformGrid3D module¶

Module contents¶