solvers Package

solvers Package

exception fipy.solvers.SolverConvergenceWarning(solver, iter, relres)

Bases: exceptions.Warning

exception fipy.solvers.MaximumIterationWarning(solver, iter, relres)

Bases: fipy.solvers.solver.SolverConvergenceWarning

exception fipy.solvers.PreconditionerWarning(solver, iter, relres)

Bases: fipy.solvers.solver.SolverConvergenceWarning

exception fipy.solvers.IllConditionedPreconditionerWarning(solver, iter, relres)

Bases: fipy.solvers.solver.PreconditionerWarning

exception fipy.solvers.PreconditionerNotPositiveDefiniteWarning(solver, iter, relres)

Bases: fipy.solvers.solver.PreconditionerWarning

exception fipy.solvers.MatrixIllConditionedWarning(solver, iter, relres)

Bases: fipy.solvers.solver.SolverConvergenceWarning

exception fipy.solvers.StagnatedSolverWarning(solver, iter, relres)

Bases: fipy.solvers.solver.SolverConvergenceWarning

exception fipy.solvers.ScalarQuantityOutOfRangeWarning(solver, iter, relres)

Bases: fipy.solvers.solver.SolverConvergenceWarning

class fipy.solvers.Solver(tolerance=1e-10, iterations=1000, precon=None)

Bases: object

The base LinearXSolver class.

Attention

This class is abstract. Always create one of its subclasses.

Create a Solver object.

Parameters :

• tolerance: The required error tolerance.
• iterations: The maximum number of iterative steps to perform.
• precon: Preconditioner to use. This parameter is only available for Trilinos solvers.

fipy.solvers.DefaultSolver

alias of LinearPCGSolver

fipy.solvers.DummySolver

alias of LinearPCGSolver

fipy.solvers.DefaultAsymmetricSolver

alias of LinearLUSolver

fipy.solvers.GeneralSolver

alias of LinearLUSolver

class fipy.solvers.LinearCGSSolver(precon=None, *args, **kwargs)

Bases: fipy.solvers.pysparse.pysparseSolver.PysparseSolver

The LinearCGSSolver solves a linear system of equations using the conjugate gradient squared method (CGS), a variant of the biconjugate gradient method (BiCG). CGS solves linear systems with a general non-symmetric coefficient matrix.

The LinearCGSSolver is a wrapper class for the the PySparse itsolvers.cgs() method.

Parameters :

• precon: Preconditioner to use

class fipy.solvers.LinearPCGSolver(precon=<fipy.solvers.pysparse.preconditioners.ssorPreconditioner.SsorPreconditioner instance at 0x107c8c638>, *args, **kwargs)

Bases: fipy.solvers.pysparse.pysparseSolver.PysparseSolver

The LinearPCGSolver solves a linear system of equations using the preconditioned conjugate gradient method (PCG) with symmetric successive over-relaxation (SSOR) preconditioning by default. Alternatively, Jacobi preconditioning can be specified through precon. The PCG method solves systems with a symmetric positive definite coefficient matrix.

The LinearPCGSolver is a wrapper class for the the PySparse itsolvers.pcg() and precon.ssor() methods.

Parameters :

• precon: Preconditioner to use

class fipy.solvers.LinearGMRESSolver(precon=<fipy.solvers.pysparse.preconditioners.jacobiPreconditioner.JacobiPreconditioner instance at 0x107c8c7e8>, *args, **kwargs)

Bases: fipy.solvers.pysparse.pysparseSolver.PysparseSolver

The LinearGMRESSolver solves a linear system of equations using the generalised minimal residual method (GMRES) with Jacobi preconditioning. GMRES solves systems with a general non-symmetric coefficient matrix.

The LinearGMRESSolver is a wrapper class for the the PySparse itsolvers.gmres() and precon.jacobi() methods.

Parameters :

• precon: Preconditioner to use

class fipy.solvers.LinearLUSolver(tolerance=1e-10, iterations=10, maxIterations=10, precon=None)

Bases: fipy.solvers.pysparse.pysparseSolver.PysparseSolver

The LinearLUSolver solves a linear system of equations using LU-factorisation. This method solves systems with a general non-symmetric coefficient matrix using partial pivoting.

The LinearLUSolver is a wrapper class for the the PySparse superlu.factorize() method.

Creates a LinearLUSolver.

Parameters :

• tolerance: The required error tolerance.
• iterations: The number of LU decompositions to perform. For large systems a number of iterations is generally required.
• precon: not used but maintains a common interface.

class fipy.solvers.LinearJORSolver(tolerance=1e-10, iterations=1000, relaxation=1.0)

Bases: fipy.solvers.pysparse.pysparseSolver.PysparseSolver

The LinearJORSolver solves a linear system of equations using Jacobi over-relaxation. This method solves systems with a general non-symmetric coefficient matrix.

The Solver class should not be invoked directly.

Parameters :

• tolerance: The required error tolerance.
• iterations: The maximum number of iterative steps to perform.
• relaxation: The relaxation.

class fipy.solvers.JacobiPreconditioner

Bases: fipy.solvers.pysparse.preconditioners.preconditioner.Preconditioner

Jacobi preconditioner for PySparse. Really just a wrapper class for pysparse.precon.jacobi.

Create a Preconditioner object.

class fipy.solvers.SsorPreconditioner

Bases: fipy.solvers.pysparse.preconditioners.preconditioner.Preconditioner

SSOR preconditioner for PySparse. Really just a wrapper class for pysparse.precon.jacobi.

Create a Preconditioner object.

pysparseMatrixSolver Module

solver Module

The iterative solvers may output warnings if the solution is considered unsatisfactory. If you are not interested in these warnings, you can invoke python with a warning filter such as:

$ python -Wignore::fipy.SolverConvergenceWarning myscript.py

If you are extremely concerned about your preconditioner for some reason, you can abort whenever it has problems with:

$ python -Werror::fipy.PreconditionerWarning myscript.py

exception fipy.solvers.solver.SolverConvergenceWarning(solver, iter, relres)

Bases: exceptions.Warning

exception fipy.solvers.solver.MaximumIterationWarning(solver, iter, relres)

Bases: fipy.solvers.solver.SolverConvergenceWarning

exception fipy.solvers.solver.PreconditionerWarning(solver, iter, relres)

Bases: fipy.solvers.solver.SolverConvergenceWarning

exception fipy.solvers.solver.IllConditionedPreconditionerWarning(solver, iter, relres)

Bases: fipy.solvers.solver.PreconditionerWarning

exception fipy.solvers.solver.PreconditionerNotPositiveDefiniteWarning(solver, iter, relres)

Bases: fipy.solvers.solver.PreconditionerWarning

exception fipy.solvers.solver.MatrixIllConditionedWarning(solver, iter, relres)

Bases: fipy.solvers.solver.SolverConvergenceWarning

exception fipy.solvers.solver.StagnatedSolverWarning(solver, iter, relres)

Bases: fipy.solvers.solver.SolverConvergenceWarning

exception fipy.solvers.solver.ScalarQuantityOutOfRangeWarning(solver, iter, relres)

Bases: fipy.solvers.solver.SolverConvergenceWarning

class fipy.solvers.solver.Solver(tolerance=1e-10, iterations=1000, precon=None)

Bases: object

The base LinearXSolver class.

Attention

This class is abstract. Always create one of its subclasses.

Create a Solver object.

Parameters :

• tolerance: The required error tolerance.
• iterations: The maximum number of iterative steps to perform.
• precon: Preconditioner to use. This parameter is only available for Trilinos solvers.

test Module

Subpackages

• pyAMG Package
  • pyAMG Package
  • linearCGSSolver Module
  • linearGMRESSolver Module
  • linearGeneralSolver Module
  • linearLUSolver Module
  • linearPCGSolver Module
  • smoothedAggregationSolver Module
  • Subpackages
    • preconditioners Package
      • preconditioners Package
      • smoothedAggregationPreconditioner Module
• pysparse Package
  • pysparse Package
  • linearCGSSolver Module
  • linearGMRESSolver Module
  • linearJORSolver Module
  • linearLUSolver Module
  • linearPCGSolver Module
  • pysparseSolver Module
  • Subpackages
    • preconditioners Package
      • preconditioners Package
      • jacobiPreconditioner Module
      • preconditioner Module
      • ssorPreconditioner Module
• scipy Package
  • scipy Package
  • linearBicgstabSolver Module
  • linearCGSSolver Module
  • linearGMRESSolver Module
  • linearLUSolver Module
  • linearPCGSolver Module
  • scipyKrylovSolver Module
  • scipySolver Module
• trilinos Package
  • trilinos Package
  • linearBicgstabSolver Module
  • linearCGSSolver Module
  • linearGMRESSolver Module
  • linearLUSolver Module
  • linearPCGSolver Module
  • trilinosAztecOOSolver Module
  • trilinosMLTest Module
  • trilinosNonlinearSolver Module
  • trilinosSolver Module
  • Subpackages
    • preconditioners Package
      • preconditioners Package
      • domDecompPreconditioner Module
      • icPreconditioner Module
      • jacobiPreconditioner Module
      • multilevelDDMLPreconditioner Module
      • multilevelDDPreconditioner Module
      • multilevelNSSAPreconditioner Module
      • multilevelSAPreconditioner Module
      • multilevelSGSPreconditioner Module
      • multilevelSolverSmootherPreconditioner Module
      • preconditioner Module