--- /dev/null
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2013 - 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.
+//
+// ---------------------------------------------------------------------
+
+
+
+// this function tests the correctness of the implementation of matrix free
+// matrix-vector products by comparing with the result of deal.II sparse
+// matrix. The implementation is similar to matrix_vector_stokes_noflux.cc
+// but tests edge hanging-node constraints.
+
+#include <deal.II/base/utilities.h>
+
+#include <deal.II/dofs/dof_handler.h>
+#include <deal.II/dofs/dof_renumbering.h>
+#include <deal.II/dofs/dof_tools.h>
+
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/fe/fe_system.h>
+#include <deal.II/fe/fe_values.h>
+#include <deal.II/fe/mapping_q.h>
+
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/manifold_lib.h>
+#include <deal.II/grid/tria.h>
+
+#include <deal.II/lac/affine_constraints.h>
+#include <deal.II/lac/block_sparse_matrix.h>
+#include <deal.II/lac/block_sparsity_pattern.h>
+#include <deal.II/lac/block_vector.h>
+
+#include <deal.II/matrix_free/fe_evaluation.h>
+#include <deal.II/matrix_free/matrix_free.h>
+
+#include <deal.II/numerics/vector_tools.h>
+
+#include <complex>
+#include <iostream>
+
+#include "../tests.h"
+
+
+
+template <int dim, int degree_p, typename VectorType>
+class MatrixFreeTest
+{
+public:
+ using CellIterator = typename DoFHandler<dim>::active_cell_iterator;
+ using Number = double;
+
+ MatrixFreeTest(const MatrixFree<dim, Number> &data_in)
+ : data(data_in){};
+
+ void
+ local_apply(const MatrixFree<dim, Number> & data,
+ VectorType & dst,
+ const VectorType & src,
+ const std::pair<unsigned int, unsigned int> &cell_range) const
+ {
+ using vector_t = VectorizedArray<Number>;
+ FEEvaluation<dim, degree_p + 1, degree_p + 2, dim, Number> velocity(data,
+ 0);
+ FEEvaluation<dim, degree_p, degree_p + 2, 1, Number> pressure(data, 1);
+
+ for (unsigned int cell = cell_range.first; cell < cell_range.second; ++cell)
+ {
+ velocity.reinit(cell);
+ velocity.read_dof_values(src.block(0));
+ velocity.evaluate(EvaluationFlags::gradients);
+ pressure.reinit(cell);
+ pressure.read_dof_values(src.block(1));
+ pressure.evaluate(EvaluationFlags::values);
+
+ for (unsigned int q = 0; q < velocity.n_q_points; ++q)
+ {
+ SymmetricTensor<2, dim, vector_t> sym_grad_u =
+ velocity.get_symmetric_gradient(q);
+ vector_t pres = pressure.get_value(q);
+ vector_t div = -trace(sym_grad_u);
+ pressure.submit_value(div, q);
+
+ // subtract p * I
+ for (unsigned int d = 0; d < dim; ++d)
+ sym_grad_u[d][d] -= pres;
+
+ velocity.submit_symmetric_gradient(sym_grad_u, q);
+ }
+
+ velocity.integrate(EvaluationFlags::gradients);
+ velocity.distribute_local_to_global(dst.block(0));
+ pressure.integrate(EvaluationFlags::values);
+ pressure.distribute_local_to_global(dst.block(1));
+ }
+ }
+
+
+ void
+ vmult(VectorType &dst, const VectorType &src) const
+ {
+ dst = 0;
+ data.cell_loop(&MatrixFreeTest<dim, degree_p, VectorType>::local_apply,
+ this,
+ dst,
+ src);
+ };
+
+private:
+ const MatrixFree<dim, Number> &data;
+};
+
+
+
+template <int dim, int fe_degree>
+void
+test()
+{
+ Triangulation<dim> triangulation;
+ GridGenerator::hyper_cube(triangulation);
+ triangulation.refine_global();
+ for (const auto &cell : triangulation.active_cell_iterators())
+ if (cell->index() > 0)
+ cell->set_refine_flag();
+ triangulation.execute_coarsening_and_refinement();
+
+ MappingQ<dim> mapping(3);
+ FE_Q<dim> fe_u_scal(fe_degree + 1);
+ FESystem<dim> fe_u(fe_u_scal, dim);
+ FE_Q<dim> fe_p(fe_degree);
+ FESystem<dim> fe(fe_u_scal, dim, fe_p, 1);
+ DoFHandler<dim> dof_handler_u(triangulation);
+ DoFHandler<dim> dof_handler_p(triangulation);
+ DoFHandler<dim> dof_handler(triangulation);
+
+ MatrixFree<dim, double> mf_data;
+
+ AffineConstraints<double> constraints, constraints_u, constraints_p;
+
+ BlockSparsityPattern sparsity_pattern;
+ BlockSparseMatrix<double> system_matrix;
+
+ BlockVector<double> solution;
+ BlockVector<double> system_rhs;
+ BlockVector<double> mf_solution;
+
+ dof_handler.distribute_dofs(fe);
+ dof_handler_u.distribute_dofs(fe_u);
+ dof_handler_p.distribute_dofs(fe_p);
+ std::vector<unsigned int> stokes_sub_blocks(dim + 1, 0);
+ stokes_sub_blocks[dim] = 1;
+ DoFRenumbering::component_wise(dof_handler, stokes_sub_blocks);
+
+ std::set<types::boundary_id> no_normal_flux_boundaries;
+ no_normal_flux_boundaries.insert(0);
+ no_normal_flux_boundaries.insert(1);
+ DoFTools::make_hanging_node_constraints(dof_handler, constraints);
+ VectorTools::compute_no_normal_flux_constraints(
+ dof_handler, 0, no_normal_flux_boundaries, constraints, mapping);
+ constraints.close();
+ DoFTools::make_hanging_node_constraints(dof_handler_u, constraints_u);
+ VectorTools::compute_no_normal_flux_constraints(
+ dof_handler_u, 0, no_normal_flux_boundaries, constraints_u, mapping);
+ constraints_u.close();
+ DoFTools::make_hanging_node_constraints(dof_handler_p, constraints_p);
+ constraints_p.close();
+
+ const std::vector<types::global_dof_index> dofs_per_block =
+ DoFTools::count_dofs_per_fe_block(dof_handler, stokes_sub_blocks);
+
+ // std::cout << "Number of active cells: "
+ // << triangulation.n_active_cells()
+ // << std::endl
+ // << "Number of degrees of freedom: "
+ // << dof_handler.n_dofs()
+ // << " (" << n_u << '+' << n_p << ')'
+ // << std::endl;
+
+ {
+ BlockDynamicSparsityPattern csp(2, 2);
+
+ for (unsigned int d = 0; d < 2; ++d)
+ for (unsigned int e = 0; e < 2; ++e)
+ csp.block(d, e).reinit(dofs_per_block[d], dofs_per_block[e]);
+
+ csp.collect_sizes();
+
+ DoFTools::make_sparsity_pattern(dof_handler, csp, constraints, false);
+ sparsity_pattern.copy_from(csp);
+ }
+
+ system_matrix.reinit(sparsity_pattern);
+
+ // this is from step-22
+ {
+ QGauss<dim> quadrature_formula(fe_degree + 2);
+
+ FEValues<dim> fe_values(mapping,
+ fe,
+ quadrature_formula,
+ update_values | update_JxW_values |
+ update_gradients);
+
+ const unsigned int dofs_per_cell = fe.dofs_per_cell;
+ const unsigned int n_q_points = quadrature_formula.size();
+
+ FullMatrix<double> local_matrix(dofs_per_cell, dofs_per_cell);
+
+ std::vector<types::global_dof_index> local_dof_indices(dofs_per_cell);
+
+ const FEValuesExtractors::Vector velocities(0);
+ const FEValuesExtractors::Scalar pressure(dim);
+
+ std::vector<SymmetricTensor<2, dim>> phi_grads_u(dofs_per_cell);
+ std::vector<double> div_phi_u(dofs_per_cell);
+ std::vector<double> phi_p(dofs_per_cell);
+
+ typename DoFHandler<dim>::active_cell_iterator cell =
+ dof_handler.begin_active(),
+ endc = dof_handler.end();
+ for (; cell != endc; ++cell)
+ {
+ fe_values.reinit(cell);
+ local_matrix = 0;
+
+ for (unsigned int q = 0; q < n_q_points; ++q)
+ {
+ for (unsigned int k = 0; k < dofs_per_cell; ++k)
+ {
+ phi_grads_u[k] = fe_values[velocities].symmetric_gradient(k, q);
+ div_phi_u[k] = fe_values[velocities].divergence(k, q);
+ phi_p[k] = fe_values[pressure].value(k, q);
+ }
+
+ for (unsigned int i = 0; i < dofs_per_cell; ++i)
+ {
+ for (unsigned int j = 0; j <= i; ++j)
+ {
+ local_matrix(i, j) +=
+ (phi_grads_u[i] * phi_grads_u[j] -
+ div_phi_u[i] * phi_p[j] - phi_p[i] * div_phi_u[j]) *
+ fe_values.JxW(q);
+ }
+ }
+ }
+ for (unsigned int i = 0; i < dofs_per_cell; ++i)
+ for (unsigned int j = i + 1; j < dofs_per_cell; ++j)
+ local_matrix(i, j) = local_matrix(j, i);
+
+ cell->get_dof_indices(local_dof_indices);
+ constraints.distribute_local_to_global(local_matrix,
+ local_dof_indices,
+ system_matrix);
+ }
+ }
+
+
+ solution.reinit(2);
+ for (unsigned int d = 0; d < 2; ++d)
+ solution.block(d).reinit(dofs_per_block[d]);
+ solution.collect_sizes();
+
+ system_rhs.reinit(solution);
+ mf_solution.reinit(solution);
+
+ // fill system_rhs with random numbers
+ for (unsigned int j = 0; j < system_rhs.block(0).size(); ++j)
+ if (constraints_u.is_constrained(j) == false)
+ {
+ const double val = -1 + 2. * random_value<double>();
+ system_rhs.block(0)(j) = val;
+ }
+ for (unsigned int j = 0; j < system_rhs.block(1).size(); ++j)
+ if (constraints_p.is_constrained(j) == false)
+ {
+ const double val = -1 + 2. * random_value<double>();
+ system_rhs.block(1)(j) = val;
+ }
+
+ // setup matrix-free structure
+ {
+ std::vector<const DoFHandler<dim> *> dofs;
+ dofs.push_back(&dof_handler_u);
+ dofs.push_back(&dof_handler_p);
+ std::vector<const AffineConstraints<double> *> constraints;
+ constraints.push_back(&constraints_u);
+ constraints.push_back(&constraints_p);
+ QGauss<1> quad(fe_degree + 2);
+ // no parallelism
+ mf_data.reinit(mapping,
+ dofs,
+ constraints,
+ quad,
+ typename MatrixFree<dim>::AdditionalData(
+ MatrixFree<dim>::AdditionalData::none));
+ }
+
+ system_matrix.vmult(solution, system_rhs);
+
+ MatrixFreeTest<dim, fe_degree, BlockVector<double>> mf(mf_data);
+ mf.vmult(mf_solution, system_rhs);
+
+ // Verification
+ mf_solution -= solution;
+ const double error = mf_solution.linfty_norm();
+ const double relative = solution.linfty_norm();
+ deallog << "Verification fe degree " << fe_degree << ": " << error / relative
+ << std::endl
+ << std::endl;
+}
+
+
+
+int
+main()
+{
+ initlog();
+ deallog << std::setprecision(3);
+
+ {
+ deallog << std::endl << "Test with doubles" << std::endl << std::endl;
+ deallog.push("2d");
+ test<2, 1>();
+ test<2, 2>();
+ test<2, 3>();
+ deallog.pop();
+ deallog.push("3d");
+ test<3, 1>();
+ deallog.pop();
+ }
+}
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