--- /dev/null
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2021 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE.md at
+// the top level directory of deal.II.
+//
+// ---------------------------------------------------------------------
+
+// Step-06 on a simplex mesh.
+//
+// The following changes had to be made due to incompatibilities:
+// - Manifolds are disabled
+// All manifold ids from the triangulation object generated with
+// GridGenerator::hyper_ball() had to be removed
+// - Error estimation has to be skipped
+// KellyErrorEstimator requires QProjector::project_to_all_subfaces()
+// to work with triangles
+// - GridOut::write_gnuplot() has been skipped
+
+
+#define USE_SIMPLEX
+// #define OUTPUT_RESULTS
+
+
+#ifdef USE_SIMPLEX
+# include <deal.II/base/types.h>
+
+# include <deal.II/simplex/fe_lib.h>
+# include <deal.II/simplex/quadrature_lib.h>
+#else
+# include <deal.II/base/quadrature_lib.h>
+
+# include <deal.II/fe/fe_q.h>
+#endif
+
+
+#ifdef OUTPUT_RESULTS
+# include <deal.II/numerics/data_out.h>
+
+# include <fstream>
+#endif
+
+
+#include <deal.II/dofs/dof_handler.h>
+#include <deal.II/dofs/dof_tools.h>
+
+#include <deal.II/fe/fe_values.h>
+#include <deal.II/fe/mapping_fe.h>
+
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/grid_refinement.h>
+#include <deal.II/grid/tria.h>
+
+#include <deal.II/lac/affine_constraints.h>
+#include <deal.II/lac/dynamic_sparsity_pattern.h>
+#include <deal.II/lac/full_matrix.h>
+#include <deal.II/lac/precondition.h>
+#include <deal.II/lac/solver_cg.h>
+#include <deal.II/lac/sparse_matrix.h>
+#include <deal.II/lac/vector.h>
+
+#include <deal.II/numerics/error_estimator.h>
+#include <deal.II/numerics/vector_tools.h>
+
+#include "../tests.h"
+
+
+
+using namespace dealii;
+
+
+template <int dim>
+class Step6
+{
+public:
+ Step6();
+
+ void
+ run();
+
+private:
+ void
+ setup_system();
+ void
+ assemble_system();
+ void
+ solve();
+ void
+ refine_grid();
+ void
+ output_results(const unsigned int cycle) const;
+
+#ifdef USE_SIMPLEX
+ Simplex::FE_P<dim> fe;
+#else
+ FE_Q<dim> fe;
+#endif
+
+ Triangulation<dim> triangulation;
+ DoFHandler<dim> dof_handler;
+
+ AffineConstraints<double> constraints;
+
+ SparseMatrix<double> system_matrix;
+ SparsityPattern sparsity_pattern;
+
+ Vector<double> solution;
+ Vector<double> system_rhs;
+};
+
+
+
+template <int dim>
+double
+coefficient(const Point<dim> &p)
+{
+ if (p.square() < 0.5 * 0.5)
+ return 20;
+ else
+ return 1;
+}
+
+
+
+template <int dim>
+Step6<dim>::Step6()
+ : fe(2)
+ , dof_handler(triangulation)
+{}
+
+
+
+template <int dim>
+void
+Step6<dim>::setup_system()
+{
+ dof_handler.distribute_dofs(fe);
+
+ solution.reinit(dof_handler.n_dofs());
+ system_rhs.reinit(dof_handler.n_dofs());
+
+ constraints.clear();
+ DoFTools::make_hanging_node_constraints(dof_handler, constraints);
+ VectorTools::interpolate_boundary_values(dof_handler,
+ 0,
+ Functions::ZeroFunction<dim>(),
+ constraints);
+ constraints.close();
+
+ DynamicSparsityPattern dsp(dof_handler.n_dofs());
+ DoFTools::make_sparsity_pattern(dof_handler,
+ dsp,
+ constraints,
+ /*keep_constrained_dofs = */ false);
+ sparsity_pattern.copy_from(dsp);
+ system_matrix.reinit(sparsity_pattern);
+}
+
+
+
+template <int dim>
+void
+Step6<dim>::assemble_system()
+{
+#ifdef USE_SIMPLEX
+ const Simplex::QGauss<dim> quadrature_formula(fe.degree + 1);
+#else
+ const QGauss<dim> quadrature_formula(fe.degree + 1);
+#endif
+
+ MappingFE<dim> mapping(fe);
+ FEValues<dim> fe_values(mapping,
+ fe,
+ quadrature_formula,
+ update_values | update_gradients |
+ update_quadrature_points | 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())
+ {
+ cell_matrix = 0;
+ cell_rhs = 0;
+
+ fe_values.reinit(cell);
+
+ for (const unsigned int q_index : fe_values.quadrature_point_indices())
+ {
+ const double current_coefficient =
+ coefficient(fe_values.quadrature_point(q_index));
+ for (const unsigned int i : fe_values.dof_indices())
+ {
+ for (const unsigned int j : fe_values.dof_indices())
+ cell_matrix(i, j) +=
+ (current_coefficient * // a(x_q)
+ 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
+ cell_rhs(i) += (1.0 * // f(x)
+ fe_values.shape_value(i, q_index) * // phi_i(x_q)
+ fe_values.JxW(q_index)); // dx
+ }
+ }
+
+ cell->get_dof_indices(local_dof_indices);
+ constraints.distribute_local_to_global(
+ cell_matrix, cell_rhs, local_dof_indices, system_matrix, system_rhs);
+ }
+}
+
+
+
+template <int dim>
+void
+Step6<dim>::solve()
+{
+ SolverControl solver_control(1000, 1e-12);
+ SolverCG<Vector<double>> solver(solver_control);
+
+ PreconditionSSOR<SparseMatrix<double>> preconditioner;
+ preconditioner.initialize(system_matrix, 1.2);
+
+ solver.solve(system_matrix, solution, system_rhs, preconditioner);
+
+ constraints.distribute(solution);
+}
+
+
+
+template <int dim>
+void
+Step6<dim>::refine_grid()
+{
+ Vector<float> estimated_error_per_cell(triangulation.n_active_cells());
+
+#if false
+# ifdef USE_SIMPLEX
+ KellyErrorEstimator<dim>::estimate(MappingFE<dim>(fe),
+ dof_handler,
+ Simplex::QGauss<dim - 1>(fe.degree + 1),
+ {},
+ solution,
+ estimated_error_per_cell);
+# else
+ KellyErrorEstimator<dim>::estimate(MappingFE<dim>(fe),
+ dof_handler,
+ QGauss<dim - 1>(fe.degree + 1),
+ {},
+ solution,
+ estimated_error_per_cell);
+# endif
+
+ GridRefinement::refine_and_coarsen_fixed_number(triangulation,
+ estimated_error_per_cell,
+ 0.3,
+ 0.03);
+#else
+ // incompatibility: KellyErrorEstimator does not yet work for simplices
+ // instead, we will mark cells for refinement by hand
+ for (const auto &cell : triangulation.active_cell_iterators())
+ for (unsigned int v = 0; v < cell->n_vertices(); ++v)
+ {
+ const double vertex_square = cell->vertex(v).square();
+ if (vertex_square > 0.48 * 0.48 && vertex_square < 0.52 * 0.52)
+ cell->set_refine_flag();
+ }
+#endif
+
+ triangulation.execute_coarsening_and_refinement();
+}
+
+
+
+template <int dim>
+void
+Step6<dim>::output_results(const unsigned int cycle) const
+{
+#ifdef OUTPUT_RESULTS
+ {
+ DataOut<dim> data_out;
+ data_out.attach_dof_handler(dof_handler);
+ data_out.add_data_vector(solution, "solution");
+ data_out.build_patches(MappingFE<dim>(fe));
+
+ std::ofstream output("solution-" + std::to_string(cycle) + ".vtu");
+ data_out.write_vtu(output);
+ }
+#else
+ (void)cycle;
+#endif
+}
+
+
+
+template <int dim>
+void
+Step6<dim>::run()
+{
+ for (unsigned int cycle = 0; cycle < 5; ++cycle)
+ {
+ deallog << "Cycle " << cycle << ':' << std::endl;
+
+ if (cycle == 0)
+ {
+#ifdef USE_SIMPLEX
+ Triangulation<dim> tria_quad;
+ GridGenerator::hyper_ball(tria_quad);
+
+ // incompatibility: remove all manifold ids
+ for (const auto &cell : tria_quad.active_cell_iterators())
+ {
+ cell->set_manifold_id(numbers::flat_manifold_id);
+ for (const auto &face : cell->face_iterators())
+ face->set_manifold_id(numbers::flat_manifold_id);
+ }
+
+ GridGenerator::convert_hypercube_to_simplex_mesh(tria_quad,
+ triangulation);
+#else
+ GridGenerator::hyper_ball(triangulation);
+#endif
+
+ triangulation.refine_global(1);
+ }
+ else
+ refine_grid();
+
+ deallog << " Number of active cells: "
+ << triangulation.n_active_cells() << std::endl;
+
+ setup_system();
+
+ deallog << " Number of degrees of freedom: " << dof_handler.n_dofs()
+ << std::endl;
+
+ assemble_system();
+ solve();
+ output_results(cycle);
+ }
+
+ deallog << "OK" << std::endl;
+}
+
+
+
+int
+main()
+{
+ initlog();
+
+ try
+ {
+ Step6<2> laplace_problem_2d;
+ laplace_problem_2d.run();
+ }
+ catch (std::exception &exc)
+ {
+ std::cerr << std::endl
+ << std::endl
+ << "----------------------------------------------------"
+ << std::endl;
+ std::cerr << "Exception on processing: " << std::endl
+ << exc.what() << std::endl
+ << "Aborting!" << std::endl
+ << "----------------------------------------------------"
+ << std::endl;
+ return 1;
+ }
+ catch (...)
+ {
+ std::cerr << std::endl
+ << std::endl
+ << "----------------------------------------------------"
+ << std::endl;
+ std::cerr << "Unknown exception!" << std::endl
+ << "Aborting!" << std::endl
+ << "----------------------------------------------------"
+ << std::endl;
+ return 1;
+ }
+ return 0;
+}
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