cashocs.nonlinear_solvers.linear_solve#

cashocs.nonlinear_solvers.linear_solve(
linear_form: ufl.Form,
u: fenics.Function,
bcs: fenics.DirichletBC | list[fenics.DirichletBC],
ksp_options: _typing.KspOption | None = None,
preconditioner_form: ufl.Form = None,
A_tensor: fenics.PETScMatrix | None = None,
b_tensor: fenics.PETScVector | None = None,
linear_solver: _utils.linalg.LinearSolver | None = None,
) → fenics.Function[source]#

Solves a linear problem.

Parameters:

  • linear_form (ufl.Form) – The linear variational form of the problem, i.e., linear_form == 0

  • u (fenics.Function) – The function to be solved for

  • bcs (fenics.DirichletBC | list[fenics.DirichletBC]) – The boundary conditions for the problem

  • ksp_options (_typing.KspOption | None) – The options for the PETSc KSP solver, optional. Default is None, where the linear solver MUMPS is used

  • preconditioner_form (ufl.Form) – The UFL form for defining the preconditioner. Must be a bilinear form.

  • A_tensor (fenics.PETScMatrix | None) – A fenics.PETScMatrix for storing the left-hand side of the linear sub-problem.

  • b_tensor (fenics.PETScVector | None) – A fenics.PETScVector for storing the right-hand side of the linear sub-problem.

  • linear_solver (_utils.linalg.LinearSolver | None) – The linear solver used to solve the (discretized) linear problem.

Returns:

The computed solution, this overwrites the input function u.

Return type:

fenics.Function

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