Step3 Class Reference

#include <step-3.h>

Inheritance diagram for Step3:

Public Member Functions
	Step3 ()
void	run ()

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

Protected Attributes
Triangulation< 2 >	triangulation
FE_Q< 2 >	fe
DoFHandler< 2 >	dof_handler
SparsityPattern	sparsity_pattern
SparseMatrix< double >	system_matrix
Vector< double >	solution
Vector< double >	system_rhs

Friends
class	Step3Tester

Detailed Description

Definition at line 55 of file step-3.h.

Constructor & Destructor Documentation

Step3()

Step3::Step3

(

)

Definition at line 24 of file step-3.cc.

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

Member Function Documentation

run()

void Step3::run

(

)

Definition at line 133 of file step-3.cc.

{
  make_grid();
  setup_system();
  assemble_system();
  solve();
  output_results();
}

make_grid()

void Step3::make_grid ( )

protected

Definition at line 32 of file step-3.cc.

{
  GridGenerator::hyper_cube(triangulation, -1, 1);
  triangulation.refine_global(5);
  std::cout << "Number of active cells: " << triangulation.n_active_cells()
            << std::endl;
}

setup_system()

void Step3::setup_system ( )

protected

Definition at line 43 of file step-3.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()

void Step3::assemble_system ( )

protected

Definition at line 59 of file step-3.cc.

{
  QGauss<2>          quadrature_formula(fe.degree + 1);
  FEValues<2>        fe_values(fe,
                        quadrature_formula,
                        update_values | update_gradients | update_JxW_values);
  const unsigned int dofs_per_cell = fe.n_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
          for (const unsigned int i : fe_values.dof_indices())
            cell_rhs(i) += (fe_values.shape_value(i, q_index) * // phi_i(x_q)
                            1. *                                // 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));
      for (const unsigned int i : fe_values.dof_indices())
        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,
                                           Functions::ZeroFunction<2>(),
                                           boundary_values);
  MatrixTools::apply_boundary_values(boundary_values,
                                     system_matrix,
                                     solution,
                                     system_rhs);
}

solve()

void Step3::solve ( )

protected

Definition at line 110 of file step-3.cc.

{
  SolverControl            solver_control(1000, 1e-12);
  SolverCG<Vector<double>> solver(solver_control);
  solver.solve(system_matrix, solution, system_rhs, PreconditionIdentity());
}

output_results()

void Step3::output_results ( ) const

protected

Definition at line 120 of file step-3.cc.

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

Friends And Related Function Documentation

Step3Tester

friend class Step3Tester

friend

Definition at line 82 of file step-3.h.

Member Data Documentation

triangulation

Triangulation<2> Step3::triangulation

protected

Definition at line 74 of file step-3.h.

fe

FE_Q<2> Step3::fe

protected

Definition at line 75 of file step-3.h.

dof_handler

DoFHandler<2> Step3::dof_handler

protected

Definition at line 76 of file step-3.h.

sparsity_pattern

SparsityPattern Step3::sparsity_pattern

protected

Definition at line 77 of file step-3.h.

system_matrix

SparseMatrix<double> Step3::system_matrix

protected

Definition at line 78 of file step-3.h.

solution

Vector<double> Step3::solution

protected

Definition at line 79 of file step-3.h.

system_rhs

Vector<double> Step3::system_rhs

protected

Definition at line 80 of file step-3.h.

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

• labs/lab-03/include/step-3.h
• labs/lab-03/source/step-3.cc