From 3d1c0042f44c6e40e7b170aea3ff2ccce540dc39 Mon Sep 17 00:00:00 2001 From: Elias Dejene Date: Sat, 2 Jan 2021 13:23:06 +0100 Subject: [PATCH] Add tutorial step-03 with simplex support. --- tests/simplex/step-03.cc | 245 ++++++++ .../step-03.with_simplex_support=on.output | 532 ++++++++++++++++++ 2 files changed, 777 insertions(+) create mode 100644 tests/simplex/step-03.cc create mode 100644 tests/simplex/step-03.with_simplex_support=on.output diff --git a/tests/simplex/step-03.cc b/tests/simplex/step-03.cc new file mode 100644 index 0000000000..ae8a03e29d --- /dev/null +++ b/tests/simplex/step-03.cc @@ -0,0 +1,245 @@ +// --------------------------------------------------------------------- +// +// 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 +#include + +#include +#include +#include + +#include +#include +#include +#include + +#include +#include +#include +#include +#include + +#include +#include +#include +#include +#include +#include + +#include +#include +#include + +#include +#include +#include + +#include +#include + +#include "../tests.h" + +using namespace dealii; + +template +class Step3 +{ +public: + Step3(); + void + run(); + +private: + void + make_grid(); + void + setup_system(); + void + assemble_system(); + void + solve(); + void + output_results() const; + + Triangulation triangulation; + unsigned int fe_degree; + Simplex::FE_P fe; + Simplex::QGauss quadrature_formula; + + DoFHandler dof_handler; + MappingFE mapping; + + SparsityPattern sparsity_pattern; + SparseMatrix system_matrix; + + Vector solution; + Vector system_rhs; +}; + +template +Step3::Step3() + : fe_degree(1) + , fe(fe_degree) + , quadrature_formula(fe_degree + 1) + , dof_handler(triangulation) + , mapping(Simplex::FE_P(1)) +{} + +template +void +Step3::make_grid() +{ + Triangulation temp_tria; + + GridGenerator::subdivided_hyper_cube(temp_tria, 2); + GridGenerator::convert_hypercube_to_simplex_mesh(temp_tria, + triangulation); + triangulation.refine_global(1); + + deallog << "Number of active cells: " << triangulation.n_active_cells() + << std::endl; +} + +template +void +Step3::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 +void +Step3::assemble_system() +{ + FEValues 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 cell_matrix(dofs_per_cell, dofs_per_cell); + Vector cell_rhs(dofs_per_cell); + + std::vector 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 boundary_values; + VectorTools::interpolate_boundary_values( + mapping, dof_handler, 0, Functions::ZeroFunction(), boundary_values); + MatrixTools::apply_boundary_values(boundary_values, + system_matrix, + solution, + system_rhs); +} + +template +void +Step3::solve() +{ + SolverControl solver_control(1000, 1e-12); + + SolverCG> solver(solver_control); + solver.solve(system_matrix, solution, system_rhs, PreconditionIdentity()); +} + +template +void +Step3::output_results() const +{ + DataOut 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 +void +Step3::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; +} diff --git a/tests/simplex/step-03.with_simplex_support=on.output b/tests/simplex/step-03.with_simplex_support=on.output new file mode 100644 index 0000000000..62ee19c10f --- /dev/null +++ b/tests/simplex/step-03.with_simplex_support=on.output @@ -0,0 +1,532 @@ + +DEAL::Number of active cells: 128 +DEAL::Number of degrees of freedom: 81 +DEAL:cg::Starting value 0.109746 +DEAL:cg::Convergence step 9 value 1.24504e-18 +# vtk DataFile Version 3.0 +#This file was generated +ASCII +DATASET UNSTRUCTURED_GRID + +POINTS 384 double +0.00000 0.00000 0 +0.125000 0.00000 0 +0.00000 0.125000 0 +0.125000 0.00000 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