--- /dev/null
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2020 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-03 on a simplex mesh. Following incompatible modifications had to be
+// made:
+// - Change the FE_Q to Simplex::FE_P.
+// - Change QGauss to Simplex::QGauss.
+// - Use MappingFE (Do not use default mapping).
+// - Convert triangulation to a triangulation based on simplices.
+
+
+#include <deal.II/base/function.h>
+#include <deal.II/base/quadrature_lib.h>
+
+#include <deal.II/dofs/dof_accessor.h>
+#include <deal.II/dofs/dof_handler.h>
+#include <deal.II/dofs/dof_tools.h>
+
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/fe/fe_values.h>
+#include <deal.II/fe/mapping_fe.h>
+#include <deal.II/fe/mapping_q.h>
+
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/grid_out.h>
+#include <deal.II/grid/tria.h>
+#include <deal.II/grid/tria_accessor.h>
+#include <deal.II/grid/tria_iterator.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/data_out.h>
+#include <deal.II/numerics/matrix_tools.h>
+#include <deal.II/numerics/vector_tools.h>
+
+#include <deal.II/simplex/fe_lib.h>
+#include <deal.II/simplex/grid_generator.h>
+#include <deal.II/simplex/quadrature_lib.h>
+
+#include <fstream>
+#include <iostream>
+
+#include "../tests.h"
+
+using namespace dealii;
+
+template <int dim>
+class Step3
+{
+public:
+ Step3();
+ void
+ run();
+
+private:
+ void
+ make_grid();
+ void
+ setup_system();
+ void
+ assemble_system();
+ void
+ solve();
+ void
+ output_results() const;
+
+ Triangulation<dim, dim> triangulation;
+ unsigned int fe_degree;
+ Simplex::FE_P<dim> fe;
+ Simplex::QGauss<dim> quadrature_formula;
+
+ DoFHandler<dim> dof_handler;
+ MappingFE<dim> mapping;
+
+ SparsityPattern sparsity_pattern;
+ SparseMatrix<double> system_matrix;
+
+ Vector<double> solution;
+ Vector<double> system_rhs;
+};
+
+template <int dim>
+Step3<dim>::Step3()
+ : fe_degree(1)
+ , fe(fe_degree)
+ , quadrature_formula(fe_degree + 1)
+ , dof_handler(triangulation)
+ , mapping(Simplex::FE_P<dim>(1))
+{}
+
+template <int dim>
+void
+Step3<dim>::make_grid()
+{
+ Triangulation<dim, dim> temp_tria;
+
+ GridGenerator::subdivided_hyper_cube(temp_tria, 2);
+ GridGenerator::convert_hypercube_to_simplex_mesh<dim, dim>(temp_tria,
+ triangulation);
+ triangulation.refine_global(1);
+
+ deallog << "Number of active cells: " << triangulation.n_active_cells()
+ << std::endl;
+}
+
+template <int dim>
+void
+Step3<dim>::setup_system()
+{
+ dof_handler.distribute_dofs(fe);
+ deallog << "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());
+}
+
+template <int dim>
+void
+Step3<dim>::assemble_system()
+{
+ FEValues<dim> fe_values(mapping,
+ 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(
+ mapping, dof_handler, 0, Functions::ZeroFunction<dim>(), boundary_values);
+ MatrixTools::apply_boundary_values(boundary_values,
+ system_matrix,
+ solution,
+ system_rhs);
+}
+
+template <int dim>
+void
+Step3<dim>::solve()
+{
+ SolverControl solver_control(1000, 1e-12);
+
+ SolverCG<Vector<double>> solver(solver_control);
+ solver.solve(system_matrix, solution, system_rhs, PreconditionIdentity());
+}
+
+template <int dim>
+void
+Step3<dim>::output_results() const
+{
+ DataOut<dim> data_out;
+ data_out.attach_dof_handler(dof_handler);
+ data_out.add_data_vector(solution, "solution");
+ data_out.build_patches(mapping);
+
+ data_out.write_vtk(deallog.get_file_stream());
+}
+
+template <int dim>
+void
+Step3<dim>::run()
+{
+ make_grid();
+ setup_system();
+ assemble_system();
+ solve();
+ output_results();
+}
+
+
+int
+main()
+{
+ initlog();
+
+ deallog.depth_console(2);
+
+ Step3<2> laplace_problem;
+ laplace_problem.run();
+
+ return 0;
+}
projects / dealii.git / commitdiff