cashocs.nonlinear_solvers.linear_solver.linear_solve

cashocs.nonlinear_solvers.linear_solver.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

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