Step4< dim > Class Template Reference

Public Member Functions
	Step4 ()
void	run ()

Private Member Functions
void	make_grid ()
void	setup_system ()
void	assemble_system ()
void	solve ()
void	output_results () const

Private Attributes
Triangulation< dim >	triangulation
FE_Q< dim >	fe
DoFHandler< dim >	dof_handler
SparsityPattern	sparsity_pattern
SparseMatrix< double >	system_matrix
Vector< double >	solution
Vector< double >	system_rhs

Detailed Description

template<int dim>
class Step4< dim >

Definition at line 49 of file step-4.cc.

Constructor & Destructor Documentation

Step4()

template<int dim>

Step4< dim >::Step4

Definition at line 117 of file step-4.cc.

  : fe(1)
  , dof_handler(triangulation)
{}

Member Function Documentation

run()

template<int dim>

void Step4< dim >::run

Definition at line 233 of file step-4.cc.

{
  std::cout << "Solving problem in " << dim << " space dimensions."
            << std::endl;
  make_grid();
  setup_system();
  assemble_system();
  solve();
  output_results();
}

make_grid()

template<int dim>

void Step4< dim >::make_grid

private

Definition at line 125 of file step-4.cc.

{
  GridGenerator::hyper_cube(triangulation, -1, 1);
  triangulation.refine_global(4);
  std::cout << "   Number of active cells: " << triangulation.n_active_cells()
            << std::endl
            << "   Total number of cells: " << triangulation.n_cells()
            << std::endl;
}

setup_system()

template<int dim>

void Step4< dim >::setup_system

private

Definition at line 138 of file step-4.cc.

{
  dof_handler.distribute_dofs(fe);
  std::cout << "   Number of degrees of freedom: " << dof_handler.n_dofs()
            << std::endl;
  DynamicSparsityPattern dsp(dof_handler.n_dofs());
  DoFTools::make_sparsity_pattern(dof_handler, dsp);
  sparsity_pattern.copy_from(dsp);
  system_matrix.reinit(sparsity_pattern);
  solution.reinit(dof_handler.n_dofs());
  system_rhs.reinit(dof_handler.n_dofs());
}

assemble_system()

template<int dim>

void Step4< dim >::assemble_system

private

Definition at line 154 of file step-4.cc.

{
  QGauss<dim>        quadrature_formula(fe.degree + 1);
  RightHandSide<dim> right_hand_side;
  FEValues<dim>      fe_values(fe,
                          quadrature_formula,
                          update_values | update_gradients |
                            update_quadrature_points | update_JxW_values);
  const unsigned int dofs_per_cell = fe.dofs_per_cell;
  FullMatrix<double> cell_matrix(dofs_per_cell, dofs_per_cell);
  Vector<double>     cell_rhs(dofs_per_cell);
  std::vector<types::global_dof_index> local_dof_indices(dofs_per_cell);
  for (const auto &cell : dof_handler.active_cell_iterators())
    {
      fe_values.reinit(cell);
      cell_matrix = 0;
      cell_rhs    = 0;
      for (const unsigned int q_index : fe_values.quadrature_point_indices())
        for (const unsigned int i : fe_values.dof_indices())
          {
            for (const unsigned int j : fe_values.dof_indices())
              cell_matrix(i, j) +=
                (fe_values.shape_grad(i, q_index) * // grad phi_i(x_q)
                 fe_values.shape_grad(j, q_index) * // grad phi_j(x_q)
                 fe_values.JxW(q_index));           // dx
            const auto x_q = fe_values.quadrature_point(q_index);
            cell_rhs(i) += (fe_values.shape_value(i, q_index) * // phi_i(x_q)
                            right_hand_side.value(x_q) *        // f(x_q)
                            fe_values.JxW(q_index));            // dx
          }
      cell->get_dof_indices(local_dof_indices);
      for (const unsigned int i : fe_values.dof_indices())
        {
          for (const unsigned int j : fe_values.dof_indices())
            system_matrix.add(local_dof_indices[i],
                              local_dof_indices[j],
                              cell_matrix(i, j));
          system_rhs(local_dof_indices[i]) += cell_rhs(i);
        }
    }
  std::map<types::global_dof_index, double> boundary_values;
  VectorTools::interpolate_boundary_values(dof_handler,
                                           0,
                                           BoundaryValues<dim>(),
                                           boundary_values);
  MatrixTools::apply_boundary_values(boundary_values,
                                     system_matrix,
                                     solution,
                                     system_rhs);
}

solve()

template<int dim>

void Step4< dim >::solve

private

Definition at line 208 of file step-4.cc.

{
  SolverControl            solver_control(1000, 1e-12);
  SolverCG<Vector<double>> solver(solver_control);
  solver.solve(system_matrix, solution, system_rhs, PreconditionIdentity());
  std::cout << "   " << solver_control.last_step()
            << " CG iterations needed to obtain convergence." << std::endl;
}

output_results()

template<int dim>

void Step4< dim >::output_results

private

Definition at line 220 of file step-4.cc.

{
  DataOut<dim> data_out;
  data_out.attach_dof_handler(dof_handler);
  data_out.add_data_vector(solution, "solution");
  data_out.build_patches();
  std::ofstream output(dim == 2 ? "solution-2d.vtk" : "solution-3d.vtk");
  data_out.write_vtk(output);
}

Member Data Documentation

triangulation

template<int dim>

Triangulation<dim> Step4< dim >::triangulation

private

Definition at line 67 of file step-4.cc.

fe

template<int dim>

FE_Q<dim> Step4< dim >::fe

private

Definition at line 68 of file step-4.cc.

dof_handler

template<int dim>

DoFHandler<dim> Step4< dim >::dof_handler

private

Definition at line 69 of file step-4.cc.

sparsity_pattern

template<int dim>

SparsityPattern Step4< dim >::sparsity_pattern

private

Definition at line 70 of file step-4.cc.

system_matrix

template<int dim>

SparseMatrix<double> Step4< dim >::system_matrix

private

Definition at line 71 of file step-4.cc.

solution

template<int dim>

Vector<double> Step4< dim >::solution

private

Definition at line 72 of file step-4.cc.

system_rhs

template<int dim>

Vector<double> Step4< dim >::system_rhs

private

Definition at line 73 of file step-4.cc.

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The documentation for this class was generated from the following file:

• labs/lab-04/source/step-4.cc