cashocs.nonlinear_solvers.snes.SNESSolver#

class cashocs.nonlinear_solvers.snes.SNESSolver(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)[source]#

Bases: object

Interface for using PETSc’s SNES solver.

Initialize the SNES solver.

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. Overrides the specification in the petsc_options.

  • atol (float | None) – Absolute tolerance of the solver. Overrides the specification in the petsc_options.

  • max_iter (int | None) – Maximum number of iterations carried out by the method. Overrides the specification in the petsc_options.

  • 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.

Methods Summary

assemble_function(snes, x, f)

Interface for PETSc SNESSetFunction.

assemble_jacobian(snes, x, J, P)

Interface for PETSc SNESSetJacobian.

solve()

Solves the nonlinear problem with PETSc's SNES.

Methods Documentation

assemble_function(snes: petsc4py.PETSc.SNES, x: petsc4py.PETSc.Vec, f: petsc4py.PETSc.Vec) → None[source]#

Interface for PETSc SNESSetFunction.

Parameters:

  • snes (petsc4py.PETSc.SNES) – The SNES solver

  • x (petsc4py.PETSc.Vec) – The current iterate

  • f (petsc4py.PETSc.Vec) – The vector in which the function evaluation is stored.

Return type:

None

assemble_jacobian(snes: petsc4py.PETSc.SNES, x: petsc4py.PETSc.Vec, J: petsc4py.PETSc.Mat, P: petsc4py.PETSc.Mat) → None[source]#

Interface for PETSc SNESSetJacobian.

Parameters:

  • snes (petsc4py.PETSc.SNES) – The SNES solver.

  • x (petsc4py.PETSc.Vec) – The current iterate.

  • J (petsc4py.PETSc.Mat) – The matrix storing the Jacobian.

  • P (petsc4py.PETSc.Mat) – The matrix storing the preconditioner for the Jacobian.

Return type:

None

solve() → fenics.Function[source]#

Solves the nonlinear problem with PETSc’s SNES.

Return type:

fenics.Function