vector_fe_ex2.C File Reference

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Functions
int	main (int argc, char **argv)

Function Documentation

main()

int main	(	int	argc,
		char **	argv
	)

Definition at line 51 of file vector_fe_ex2.C.

References libMesh::DiffSolver::absolute_residual_tolerance, libMesh::EquationSystems::add_system(), libMesh::ExactSolution::attach_exact_derivs(), libMesh::ExactSolution::attach_exact_values(), libMesh::MeshTools::Generation::build_cube(), libMesh::ExactSolution::compute_error(), libMesh::default_solver_package(), libMesh::ExactSolution::extra_quadrature_order(), libMesh::ExactSolution::h1_error(), libMesh::HEX8, libMesh::TriangleWrapper::init(), libMesh::EquationSystems::init(), libMesh::DiffSolver::initial_linear_tolerance, libMesh::INVALID_SOLVER_PACKAGE, libMesh::ExactSolution::l2_error(), libMesh::DiffSolver::max_linear_iterations, libMesh::DiffSolver::max_nonlinear_iterations, mesh, libMesh::out, libMesh::EquationSystems::print_info(), libMesh::MeshBase::print_info(), libMesh::DiffSolver::quiet, libMesh::DiffSolver::relative_residual_tolerance, libMesh::DiffSolver::relative_step_tolerance, libMesh::FEMSystem::solve(), libMesh::DifferentiableSystem::time_solver, libMesh::System::variable_number(), libMesh::DiffSolver::verbose, and libMesh::MeshOutput< MT >::write_equation_systems().

{
  // Initialize libMesh.
  LibMeshInit init (argc, argv);

  // This example requires a linear solver package.
  libmesh_example_requires(libMesh::default_solver_package() != INVALID_SOLVER_PACKAGE,
                           "--enable-petsc, --enable-trilinos, or --enable-eigen");

  // Parse the input file
  GetPot infile("vector_fe_ex2.in");

  // But allow the command line to override it.
  infile.parse_command_line(argc, argv);

  // Read in parameters from the input file
  const unsigned int grid_size = infile("grid_size", 2);

  // Skip higher-dimensional examples on a lower-dimensional libMesh build
  libmesh_example_requires(3 <= LIBMESH_DIM, "2D/3D support");

  // We use Dirichlet boundary conditions here
#ifndef LIBMESH_ENABLE_DIRICHLET
  libmesh_example_requires(false, "--enable-dirichlet");
#endif

  // Create a mesh, with dimension to be overridden later, on the
  // default MPI communicator.
  Mesh mesh(init.comm());

  // Use the MeshTools::Generation mesh generator to create a uniform
  // grid on the square [-1,1]^D.  We instruct the mesh generator
  // to build a mesh of 8x8 Quad9 elements in 2D, or Hex27
  // elements in 3D.  Building these higher-order elements allows
  // us to use higher-order approximation, as in example 3.
  MeshTools::Generation::build_cube (mesh,
                                     grid_size,
                                     grid_size,
                                     grid_size,
                                     -1., 1.,
                                     -1., 1.,
                                     -1., 1.,
                                     HEX8);

  // Print information about the mesh to the screen.
  mesh.print_info();

  // Create an equation systems object.
  EquationSystems equation_systems (mesh);

  // Declare the system "Laplace" and its variables.
  LaplaceSystem & system =
    equation_systems.add_system<LaplaceSystem> ("Laplace");

  // This example only implements the steady-state problem
  system.time_solver = std::make_unique<SteadySolver>(system);

  // Initialize the system
  equation_systems.init();

  // And the nonlinear solver options
  DiffSolver & solver = *(system.time_solver->diff_solver().get());
  solver.quiet = infile("solver_quiet", true);
  solver.verbose = !solver.quiet;
  solver.max_nonlinear_iterations = infile("max_nonlinear_iterations", 15);
  solver.relative_step_tolerance = infile("relative_step_tolerance", 1.e-3);
  solver.relative_residual_tolerance = infile("relative_residual_tolerance", 0.0);
  solver.absolute_residual_tolerance = infile("absolute_residual_tolerance", 0.0);

  // And the linear solver options
  solver.max_linear_iterations = infile("max_linear_iterations", 50000);
  solver.initial_linear_tolerance = infile("initial_linear_tolerance", 1.e-3);

  // Print information about the system to the screen.
  equation_systems.print_info();

  system.solve();

  ExactSolution exact_sol(equation_systems);

  SolutionFunction soln_func(system.variable_number("u"));
  SolutionGradient soln_grad(system.variable_number("u"));

  // Build FunctionBase* containers to attach to the ExactSolution object.
  std::vector<FunctionBase<Number> *> sols(1, &soln_func);
  std::vector<FunctionBase<Gradient> *> grads(1, &soln_grad);

  exact_sol.attach_exact_values(sols);
  exact_sol.attach_exact_derivs(grads);

  // Use higher quadrature order for more accurate error results
  int extra_error_quadrature = infile("extra_error_quadrature", 2);
  exact_sol.extra_quadrature_order(extra_error_quadrature);

  // Compute the error.
  exact_sol.compute_error("Laplace", "u");

  // Print out the error values
  libMesh::out << "L2-Error is: "
               << exact_sol.l2_error("Laplace", "u")
               << std::endl;
  libMesh::out << "H1-Error is: "
               << exact_sol.h1_error("Laplace", "u")
               << std::endl;

#ifdef LIBMESH_HAVE_EXODUS_API

  // We write the file in the ExodusII format.
  ExodusII_IO(mesh).write_equation_systems("out.e", equation_systems);

#endif // #ifdef LIBMESH_HAVE_EXODUS_API

  UCDIO(mesh).write_equation_systems("out.inp", equation_systems);

  // All done.
  return 0;
}