AdaptiveNonlinearVariationalSolver.h¶

Note

The documentation on this page was automatically extracted from the DOLFIN C++ code and may need to be edited or expanded.

class AdaptiveNonlinearVariationalSolver¶

A class for goal-oriented adaptive solution of nonlinear variational problems.

For a nonlinear variational problem of the form: find u in V satisfying

F(u; v) = 0 for all v in \(\hat V\)

and a corresponding conforming discrete problem: find u_h in V_h satisfying (at least approximately)

F(u_h; v) = 0 for all v in \(\hat V_h\)

and a given goal functional M and tolerance tol, the aim is to find a V_H and a u_H in V_H satisfying the discrete problem such that

|M(u) - M(u_H)| < tol

This strategy is based on dual-weighted residual error estimators designed and automatically generated for the primal problem and subsequent h-adaptivity.

AdaptiveNonlinearVariationalSolver(std::shared_ptr<NonlinearVariationalProblem> problem, std::shared_ptr<GoalFunctional> goal)¶

Create AdaptiveNonlinearVariationalSolver (shared ptr version)

Arguments

problem (NonlinearVariationalProblem): The primal problem
goal (GoalFunctional): The goal functional

AdaptiveNonlinearVariationalSolver(std::shared_ptr<NonlinearVariationalProblem> problem, std::shared_ptr<Form> goal, std::shared_ptr<ErrorControl> control)¶

Create AdaptiveLinearVariationalSolver from variational problem, goal form and error control instance

Arguments

problem (NonlinearVariationalProblem): The primal problem
goal (Form): The goal functional
control (ErrorControl): An error controller object

std::shared_ptr<const Function> solve_primal()¶

Solve the primal problem.

Returns

Function: The solution to the primal problem

std::vector<std::shared_ptr<const DirichletBC>> extract_bcs() const¶

Extract the boundary conditions for the primal problem.

Returns

std::vector<DirichletBC>: The primal boundary conditions

double evaluate_goal(Form &M, std::shared_ptr<const Function> u) const¶

Evaluate the goal functional.

Arguments

M (Form): The functional to be evaluated
u (Function): The function at which to evaluate the functional

Returns

double: The value of M evaluated at u

void adapt_problem(std::shared_ptr<const Mesh> mesh)¶

Adapt the problem to other mesh.

Arguments

mesh (Mesh): The other mesh

std::size_t num_dofs_primal()¶

Return the number of degrees of freedom for primal problem

Returns

_std::size_t_: The number of degrees of freedom

void init(std::shared_ptr<NonlinearVariationalProblem> problem, std::shared_ptr<GoalFunctional> goal)¶

Helper function for instance initialization

Arguments

problem (NonlinearVariationalProblem): The primal problem
u (GoalFunctional): The goal functional