.. _USAGE: ========== Using FiPy ========== This document explains how to use :term:`FiPy` in a practical sense. To see the problems that :term:`FiPy` is capable of solving, you can run any of the scripts in the :ref:`examples `. .. note:: We strongly recommend you proceed through the :ref:`examples `, but at the very least work through :mod:`examples.diffusion.mesh1D` to understand the notation and basic concepts of :term:`FiPy`. We exclusively use either the unix command line or :term:`IPython` to interact with :term:`FiPy`. The commands in the :ref:`examples ` are written with the assumption that they will be executed from the command line. For instance, from within the main :term:`FiPy` directory, you can type:: $ python examples/diffusion/mesh1D.py A viewer should appear and you should be prompted through a series of examples. .. note:: From within :term:`IPython`, you would type:: >>> run examples/diffusion/mesh1D.py In order to customize the examples, or to develop your own scripts, some knowledge of Python syntax is required. We recommend you familiarize yourself with the excellent `Python tutorial`_ :cite:`PythonTutorial` or with `Dive Into Python`_ :cite:`DiveIntoPython`. .. _Python tutorial: http://docs.python.org/tut/tut.html .. _Dive Into Python: http://diveintopython.org As you gain experience, you may want to browse through the :ref:`FlagsAndEnvironmentVariables` that affect :term:`FiPy`. ------------ Testing FiPy ------------ For a general installation, :term:`FiPy` can be tested by running:: $ python -c "import fipy; fipy.test()" This command runs all the test cases in :ref:`FiPy's modules `, but doesn't include any of the tests in :ref:`FiPy's examples `. To run the test cases in both :ref:`modules ` and :ref:`examples `, use:: $ python setup.py test in an unpacked :term:`FiPy` archive. The test suite can be run with a number of different configurations depending on which solver suite is available and other factors. See :ref:`FlagsAndEnvironmentVariables` for more details. :term:`FiPy` will skip tests that depend on :ref:`OPTIONALPACKAGES` that have not been installed. For example, if :term:`Mayavi` and :term:`Gmsh` are not installed, :term:`FiPy` will warn:: !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Skipped 131 doctest examples because `gmsh` cannot be found on the $PATH Skipped 42 doctest examples because the `tvtk` package cannot be imported !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! We have a few known, intermittent failures: :trac:`#425` The test suite can freeze, usually in :mod:`examples.chemotaxis`, when running on multiple processors. This has never affected us in an actual parallel simulation, only in the test suite. :trac:`#430` When running in parallel, the tests for :class:`~fipy.terms.binaryTerm._BinaryTerm` sometimes return one erroneous result. This is not reliably reproducible and doesn't seem to have an effect on actual simulations. Although the test suite may show warnings, there should be no other errors. Any errors should be investigated or reported on the `issue tracker`_. Users can see if there are any known problems for the latest :term:`FiPy` distribution by checking `FiPy's automated test display`_. .. _FiPy's automated test display: http://build.cmi.kent.edu:8010/console .. _issue tracker: https://github.com/usnistgov/fipy/issues/new Below are a number of common `Command-line Flags`_ for testing various :term:`FiPy` configurations. Parallel Tests ============== If :term:`FiPy` is configured for :ref:`PARALLEL`, you can run the tests on multiple processor cores with:: $ mpirun -np {# of processors} python setup.py test --trilinos or:: $ mpirun -np {# of processors} python -c "import fipy; fipy.test('--trilinos')" .. _FlagsAndEnvironmentVariables: -------------------------------------------- Command-line Flags and Environment Variables -------------------------------------------- :term:`FiPy` chooses a default run time configuration based on the available packages on the system. The `Command-line Flags`_ and `Environment Variables`_ sections below describe how to override :term:`FiPy`'s default behavior. Command-line Flags ================== You can add any of the following case-insensitive flags after the name of a script you call from the command line, e.g:: $ python myFiPyScript --someflag .. cmdoption:: --inline Causes many mathematical operations to be performed in C, rather than Python, for improved performance. Requires the :mod:`scipy.weave` package. The following flags take precedence over the :envvar:`FIPY_SOLVERS` environment variable: .. cmdoption:: --pysparse Forces the use of the :ref:`PYSPARSE` solvers. .. cmdoption:: --trilinos Forces the use of the :ref:`TRILINOS` solvers, but uses :ref:`PYSPARSE` to construct the matrices. .. cmdoption:: --no-pysparse Forces the use of the :ref:`TRILINOS` solvers without any use of :ref:`PYSPARSE`. .. cmdoption:: --scipy Forces the use of the :ref:`SCIPY` solvers. .. cmdoption:: --pyamg Forces the use of the :ref:`PYAMG` preconditioners in conjunction with the :ref:`SCIPY` solvers. .. cmdoption:: --lsmlib Forces the use of the :ref:`LSMLIBDOC` level set solver. .. cmdoption:: --skfmm Forces the use of the :ref:`SCIKITFMM` level set solver. Environment Variables ===================== You can set any of the following environment variables in the manner appropriate for your shell. If you are not running in a shell (*e.g.*, you are invoking :term:`FiPy` scripts from within :term:`IPython` or IDLE), you can set these variables via the :data:`os.environ` dictionary, but you must do so before importing anything from the :mod:`fipy` package. .. envvar:: FIPY_DISPLAY_MATRIX .. currentmodule:: fipy.terms.term If present, causes the graphical display of the solution matrix of each equation at each call of :meth:`~Term.solve` or :meth:`~Term.sweep`. Setting the value to "``terms``," causes the display of the matrix for each :class:`Term` that composes the equation. Requires the :term:`Matplotlib` package. .. envvar:: FIPY_INLINE If present, causes many mathematical operations to be performed in C, rather than Python. Requires the :mod:`scipy.weave` package. .. envvar:: FIPY_INLINE_COMMENT If present, causes the addition of a comment showing the Python context that produced a particular piece of :mod:`scipy.weave` C code. Useful for debugging. .. envvar:: FIPY_SOLVERS Forces the use of the specified suite of linear solvers. Valid (case-insensitive) choices are "``pysparse``", "``trilinos``", "``no-pysparse``", "``scipy``" and "``pyamg``". .. envvar:: FIPY_VERBOSE_SOLVER If present, causes the linear solvers to print a variety of diagnostic information. .. envvar:: FIPY_VIEWER Forces the use of the specified viewer. Valid values are any :samp:`{}` from the :samp:`fipy.viewers.{}Viewer` modules. The special value of ``dummy`` will allow the script to run without displaying anything. .. envvar:: FIPY_INCLUDE_NUMERIX_ALL If present, causes the inclusion of all funcions and variables of the :mod:`~fipy.tools.numerix` module in the :mod:`fipy` namespace. .. _PARALLEL: ------------------- Solving in Parallel ------------------- :term:`FiPy` can use :term:`Trilinos` to solve equations in parallel. Most mesh classes in :mod:`fipy.meshes` can solve in parallel. This includes all "``...Grid...``" and "``...Gmsh...``" class meshes. Currently, the only remaining serial-only meshes are :class:`~fipy.meshes.tri2D.Tri2D` and :class:`~fipy.meshes.skewedGrid2D.SkewedGrid2D`. .. attention:: :term:`Trilinos` *must* be compiled with MPI support. .. attention:: :term:`FiPy` requires :ref:`MPI4PY` to work in parallel. See the :ref:`MPI4PY` installation guide. .. note:: Parallel efficiency is greatly improved by installing :term:`PySparse` in addition to :term:`Trilinos`. If :term:`PySparse` is not installed be sure to use the ``--no-pysparse`` flag when running in parallel. It should not generally be necessary to change anything in your script. Simply invoke:: $ mpirun -np {# of processors} python myScript.py --trilinos instead of:: $ python myScript.py To confirm that :term:`FiPy` and :term:`Trilinos` are properly configured to solve in parallel, the easiest way to tell is to run one of the examples, e.g.,:: $ mpirun -np 2 examples/diffusion/mesh1D.py You should see two viewers open with half the simulation running in one of them and half in the other. If this does not look right (e.g., you get two viewers, both showing the entire simultion), or if you just want to be sure, you can run a diagnostic script:: $ mpirun -np 3 python examples/parallel.py which should print out:: mpi4py: processor 0 of 3 :: PyTrilinos: processor 0 of 3 :: FiPy: 5 cells on processor 0 of 3 mpi4py: processor 1 of 3 :: PyTrilinos: processor 1 of 3 :: FiPy: 7 cells on processor 1 of 3 mpi4py: processor 2 of 3 :: PyTrilinos: processor 2 of 3 :: FiPy: 6 cells on processor 2 of 3 If there is a problem with your parallel environment, it should be clear that there is either a problem importing one of the required packages or that there is some problem with the MPI environment. For example:: mpi4py: processor 2 of 3 :: PyTrilinos: processor 0 of 1 :: FiPy: 10 cells on processor 0 of 1 [my.machine.com:69815] WARNING: There were 4 Windows created but not freed. mpi4py: processor 1 of 3 :: PyTrilinos: processor 0 of 1 :: FiPy: 10 cells on processor 0 of 1 [my.machine.com:69814] WARNING: There were 4 Windows created but not freed. mpi4py: processor 0 of 3 :: PyTrilinos: processor 0 of 1 :: FiPy: 10 cells on processor 0 of 1 [my.machine.com:69813] WARNING: There were 4 Windows created but not freed. indicates :ref:`MPI4PY` is properly communicating with MPI and is running in parallel, but that :ref:`TRILINOS` is not, and is running three separate serial environments. As a result, :term:`FiPy` is limited to three separate serial operations, too. In this instance, the problem is that although :ref:`TRILINOS` was compiled with MPI enabled, it was compiled against a different MPI library than is currently available (and which :ref:`MPI4PY` was compiled against). The solution is to rebuild :ref:`TRILINOS` against the active MPI libraries. When solving in parallel, :term:`FiPy` essentially breaks the problem up into separate sub-domains and solves them (somewhat) independently. :term:`FiPy` generally "does the right thing", but if you find that you need to do something with the entire solution, you can use ``var.``:attr:`~fipy.variables.cellVariable.CellVariable.globalValue`. .. note:: :term:`Trilinos` solvers frequently give intermediate output that :term:`FiPy` cannot suppress. The most commonly encountered messages are ``Gen_Prolongator warning : Max eigen <= 0.0`` which is not significant to :term:`FiPy`. ``Aztec status AZ_loss: loss of precision`` which indicates that there was some difficulty in solving the problem to the requested tolerance due to precision limitations, but usually does not prevent the solver from finding an adequate solution. ``Aztec status AZ_ill_cond: GMRES hessenberg ill-conditioned`` which indicates that GMRES is having trouble with the problem, and may indicate that trying a different solver or preconditioner may give more accurate results if GMRES fails. ``Aztec status AZ_breakdown: numerical breakdown`` which usually indicates serious problems solving the equation which forced the solver to stop before reaching an adequate solution. Different solvers, different preconditioners, or a less restrictive tolerance may help. .. _MeshingWithGmsh: ----------------- Meshing with Gmsh ----------------- :term:`FiPy` works with arbitrary polygonal meshes generated by :term:`Gmsh`. :term:`FiPy` provides two wrappers classes (:class:`~fipy.meshes.gmshImport.Gmsh2D` and :class:`~fipy.meshes.gmshImport.Gmsh3D`) enabling :term:`Gmsh` to be used directly from python. The classes can be instantiated with a set of :term:`Gmsh` style commands (see :mod:`examples.diffusion.circle`). The classes can also be instantiated with the path to either a :term:`Gmsh` geometry file (``.geo``) or a :term:`Gmsh` mesh file (``.msh``) (see :mod:`examples.diffusion.anisotropy`). As well as meshing arbitrary geometries, :term:`Gmsh` partitions meshes for parallel simulations. Mesh partitioning automatically occurs whenever a parallel communicator is passed to the mesh on instantiation. This is the default setting for all meshes that work in parallel including :class:`~fipy.meshes.gmshImport.Gmsh2D` and :class:`~fipy.meshes.gmshImport.Gmsh3D`. .. note:: :term:`FiPy` solution accuracy can be compromised with highly non-orthogonal or non-conjunctional meshes. .. _CoupledEquations: ---------------------------- Coupled and Vector Equations ---------------------------- Equations can now be coupled together so that the contributions from all the equations appear in a single system matrix. This results in tighter coupling for equations with spatial and temporal derivatives in more than one variable. In :term:`FiPy` equations are coupled together using the ``&`` operator:: >>> eqn0 = ... >>> eqn1 = ... >>> coupledEqn = eqn0 & eqn1 The ``coupledEqn`` will use a combined system matrix that includes four quadrants for each of the different variable and equation combinations. In previous versions of :term:`FiPy` there has been no need to specify which variable a given term acts on when generating equations. The variable is simply specified when calling ``solve`` or ``sweep`` and this functionality has been maintained in the case of single equations. However, for coupled equations the variable that a given term operates on now needs to be specified when the equation is generated. The syntax for generating coupled equations has the form:: >>> eqn0 = Term00(coeff=..., var=var0) + Term01(coeff..., var=var1) == source0 >>> eqn1 = Term10(coeff=..., var=var0) + Term11(coeff..., var=var1) == source1 >>> coupledEqn = eqn0 & eqn1 and there is now no need to pass any variables when solving:: >>> coupledEqn.solve(dt=..., solver=...) In this case the matrix system will have the form .. math:: \left( \begin{array}{c|c} \text{\ttfamily Term00} & \text{\ttfamily Term01} \\ \hline \text{\ttfamily Term10} & \text{\ttfamily Term11} \end{array} \right) \left( \begin{array}{c} \text{\ttfamily var0} \\ \hline \text{\ttfamily var1} \end{array} \right) = \left( \begin{array}{c} \text{\ttfamily source0} \\ \hline \text{\ttfamily source1} \end{array} \right) :term:`FiPy` tries to make sensible decisions regarding each term's location in the matrix and the ordering of the variable column array. For example, if ``Term01`` is a transient term then ``Term01`` would appear in the upper left diagonal and the ordering of the variable column array would be reversed. The use of coupled equation is described in detail in :mod:`examples.diffusion.coupled`. Other examples that demonstrate the use of coupled equations are :mod:`examples.phase.binaryCoupled`, :mod:`examples.phase.polyxtalCoupled` and :mod:`examples.cahnHilliard.mesh2DCoupled`. As well as coupling equations, true vector equations can now be written in :term:`FiPy` (see :mod:`examples.diffusion.coupled` for more details). .. _BoundaryConditions: ------------------- Boundary Conditions ------------------- .. currentmodule:: fipy.variables.cellVariable Applying fixed value (Dirichlet) boundary conditions ==================================================== To apply a fixed value boundary condition use the :meth:`~CellVariable.constrain` method. For example, to fix `var` to have a value of `2` along the upper surface of a domain, use >>> var.constrain(2., where=mesh.facesTop) .. note:: The old equivalent :class:`~fipy.boundaryConditions.fixedValue.FixedValue` boundary condition is now deprecated. Applying fixed gradient boundary conditions (Neumann) ===================================================== To apply a fixed Gradient boundary condition use the :attr:`~.CellVariable.faceGrad`.\ :meth:`~fipy.variables.variable.Variable.constrain` method. For example, to fix `var` to have a gradient of `(0,2)` along the upper surface of a 2D domain, use >>> var.faceGrad.constrain(((0,),(2,)), where=mesh.facesTop) If the gradient normal to the boundary (*e.g.*, :math:`\hat{n}\cdot\nabla\phi`) is to be set to a scalar value of `2`, use >>> var.faceGrad.constrain(2 * mesh.faceNormals, where=mesh.exteriorFaces) Applying fixed flux boundary conditions ======================================= Generally these can be implemented with a judicious use of :attr:`~.CellVariable.faceGrad`.\ :meth:`~fipy.variables.variable.Variable.constrain`. Failing that, an exterior flux term can be added to the equation. Firstly, set the terms' coefficients to be zero on the exterior faces, >>> diffCoeff.constrain(0., mesh.exteriorFaces) >>> convCoeff.constrain(0., mesh.exteriorFaces) then create an equation with an extra term to account for the exterior flux, >>> eqn = (TransientTerm() + ConvectionTerm(convCoeff) ... == DiffusionCoeff(diffCoeff) ... + (mesh.exteriorFaces * exteriorFlux).divergence) where `exteriorFlux` is a rank 1 :class:`~fipy.variables.faceVariable.FaceVariable`. .. note:: The old equivalent :class:`~fipy.boundaryConditions.fixedFlux.FixedFlux` boundary condition is now deprecated. Applying outlet or inlet boundary conditions ============================================ Convection terms default to a no flux boundary condition unless the exterior faces are associated with a constraint, in which case either an inlet or an outlet boundary condition is applied depending on the flow direction. Applying spatially varying boundary conditions ============================================== The use of spatial varying boundary conditions is best demonstrated with an example. Given a 2D equation in the domain :math:`0 < x < 1` and :math:`0 < y < 1` with boundary conditions, .. math:: \phi = \left\{ \begin{aligned} xy &\quad \text{on $x>1/2$ and $y>1/2$} \\ \vec{n} \cdot \vec{F} = 0 &\quad \text{elsewhere} \end{aligned} \right. where :math:`\vec{F}` represents the flux. The boundary conditions in :term:`FiPy` can be written with the following code, >>> X, Y = mesh.faceCenters >>> mask = ((X < 0.5) | (Y < 0.5)) >>> var.faceGrad.constrain(0, where=mesh.exteriorFaces & mask) >>> var.constrain(X * Y, where=mesh.exteriorFaces & ~mask) then >>> eqn.solve(...) Further demonstrations of spatially varying boundary condition can be found in :mod:`examples.diffusion.mesh20x20` and :mod:`examples.diffusion.circle` Applying internal boundary conditions ===================================== Applying internal boundary conditions can be achieved through the use of implicit and explicit sources. An equation of the form >>> eqn = TransientTerm() == DiffusionTerm() can be constrained to have a fixed internal ``value`` at a position given by ``mask`` with the following alterations >>> eqn = TransientTerm() == DiffusionTerm() - ImplicitSourceTerm(mask * largeValue) + mask * largeValue * value The parameter ``largeValue`` must be chosen to be large enough to completely dominate the matrix diagonal and the RHS vector in cells that are masked. The ``mask`` variable would typically be a ``CellVariable`` boolean constructed using the cell center values. One must be careful to distinguish between constraining internal cell values during the solve step and simply applying arbitrary constraints to a ``CellVariable``. Applying a constraint, >>> var.constrain(value, where=mask) simply fixes the returned value of ``var`` at ``mask`` to be ``value``. It does not have any effect on the implicit value of ``var`` at the ``mask`` location during the linear solve so it is not a substitute for the source term machinations described above. Future releases of :term:`FiPy` may implicitly deal with this discrepancy, but the current release does not. A simple example can be used to demonstrate this:: >>> m = Grid1D(nx=2, dx=1.) >>> var = CellVariable(mesh=m) Apply a constraint to the faces for a right side boundary condition (which works). >>> var.constrain(1., where=m.facesRight) Create the equation with the source term constraint described above >>> mask = m.x < 1. >>> largeValue = 1e+10 >>> value = 0.25 >>> eqn = DiffusionTerm() - ImplicitSourceTerm(largeValue * mask) + largeValue * mask * value and the expected value is obtained. >>> eqn.solve(var) >>> print var [ 0.25 0.75] However, if a constraint is used without the source term constraint an unexpected value is obtained >>> var.constrain(0.25, where=mask) >>> eqn = DiffusionTerm() >>> eqn.solve(var) >>> print var [ 0.25 1. ] although the left cell has the expected value as it is constrained. .. % http://thread.gmane.org/gmane.comp.python.fipy/726 % http://thread.gmane.org/gmane.comp.python.fipy/846 % \subsection{Fourth order boundary conditions} % http://thread.gmane.org/gmane.comp.python.fipy/923 % \subsection{Periodic boundary conditions} % http://thread.gmane.org/gmane.comp.python.fipy/135 % \subsection{Time dependent boundary conditions} % http://thread.gmane.org/gmane.comp.python.fipy/2 % \subsection{Internal boundary conditions} .. _RunningUnderPython3: ---------------------- Running under Python 3 ---------------------- It is possible to run :term:`FiPy` scripts under :term:`Python 3`, but there is admittedly little advantage in doing so at this time. We still develop and use :term:`FiPy` under :term:`Python` 2.x. To use, you must first convert :term:`FiPy`'s code to :term:`Python 3` syntax. From within the main :term:`FiPy` directory:: $ 2to3 --write . $ 2to3 --write --doctests_only . You can expect some harmless warnings from this conversion. The minimal prerequisites are: * :term:`NumPy` version 1.5 or greater. * :term:`SciPy` version 0.9 or greater. * :term:`Matplotlib` version 1.2 or greater (this hasn't been released yet, and we haven't been able to successfully test the :mod:`~.fipy.viewers.matplotlibViewer` classes with their development code). ------ Manual ------ You can view the manual online at or you can `download the latest manual`_ from . Alternatively, it may be possible to build a fresh copy by issuing the following command in the base directory:: $ python setup.py build_docs --pdf --html .. note:: This mechanism is intended primarily for the developers. At a minimum, you will need at least version 1.1.2 of `Sphinx `_, plus all of its prerequisites, although we build the documentation witih the latest development code (you will need hg_ installed):: $ pip install --upgrade -e hg+https://bitbucket.org/birkenfeld/sphinx#egg=sphinx We use several contributed Sphinx plugins:: $ hg clone https://bitbucket.org/birkenfeld/sphinx-contrib/ $ cd sphinx-contrib/traclinks $ python setup.py install Bibliographic citations require the `sphinxcontrib-bibtex` package. For the moment, the development versions of several packages are required to properly render our bibliography (you will need both bzr_ and git_ installed):: $ pip install -e bzr+lp:~pybtex-devs/pybtex/trunk $ pip install -e git+git@github.com:mcmtroffaes/pybtex-docutils.git#egg=pybtex-docutils $ pip install -e git+git@github.com:mcmtroffaes/sphinxcontrib-bibtex.git#egg=sphinxcontrib-bibtex .. _download the latest manual: http://www.ctcms.nist.gov/fipy/download/ .. _hg: http://mercurial.selenic.com .. _bzr: http://bazaar.canonical.com .. _git: http://git-scm.com