cashocs.nonlinear_solvers.snes.snes_solve#

cashocs.nonlinear_solvers.snes.snes_solve(
nonlinear_form: ufl.Form,
u: fenics.Function,
bcs: fenics.DirichletBC | list[fenics.DirichletBC],
derivative: ufl.Form | None = None,
petsc_options: _typing.KspOption | None = None,
shift: ufl.Form | None = None,
rtol: float | None = None,
atol: float | None = None,
max_iter: int | None = None,
A_tensor: fenics.PETScMatrix | None = None,
b_tensor: fenics.PETScVector | None = None,
preconditioner_form: ufl.Form | None = None,
) → fenics.Function[source]#

Solve a nonlinear PDE problem with PETSc SNES.

An overview over possible PETSc command line options for the SNES can be found at https://petsc.org/release/manualpages/SNES/.

Parameters:

  • nonlinear_form (ufl.Form) – The variational form of the nonlinear problem to be solved by Newton’s method.

  • u (fenics.Function) – The sought solution / initial guess. It is not assumed that the initial guess satisfies the Dirichlet boundary conditions, they are applied automatically. The method overwrites / updates this Function.

  • bcs (fenics.DirichletBC | list[fenics.DirichletBC]) – A list of DirichletBCs for the nonlinear variational problem.

  • derivative (ufl.Form | None) – The Jacobian of nonlinear_form, used for the Newton method. Default is None, and in this case the Jacobian is computed automatically with AD.

  • petsc_options (_typing.KspOption | None) – The options for PETSc SNES object.

  • shift (ufl.Form | None) – A shift term, if the right-hand side of the nonlinear problem is not zero, but shift.

  • rtol (float | None) – Relative tolerance of the solver (default is rtol = 1e-10).

  • atol (float | None) – Absolute tolerance of the solver (default is atol = 1e-10).

  • max_iter (int | None) – Maximum number of iterations carried out by the method (default is max_iter = 50).

  • 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.

  • preconditioner_form (ufl.Form | None) – A UFL form which defines the preconditioner matrix.

Returns:

The solution in form of a FEniCS Function.

Return type:

fenics.Function

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