--- /dev/null
+// ------------------------------------------------------------------------
+//
+// SPDX-License-Identifier: LGPL-2.1-or-later
+// Copyright (C) 2024 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// Part of the source code is dual licensed under Apache-2.0 WITH
+// LLVM-exception OR LGPL-2.1-or-later. Detailed license information
+// governing the source code and code contributions can be found in
+// LICENSE.md and CONTRIBUTING.md at the top level directory of deal.II.
+//
+// ------------------------------------------------------------------------
+
+
+
+// this function tests the correctness of the implementation of matrix free
+// matrix-vector products with vector-valued evaluators and their use in 1d in
+// particular using a variant of the stokes equations.
+
+#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/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"
+
+#include "create_mesh.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, 0);
+ velocity.evaluate(EvaluationFlags::gradients | EvaluationFlags::values);
+ pressure.reinit(cell);
+ pressure.read_dof_values(src, dim);
+ pressure.evaluate(EvaluationFlags::values);
+
+ for (unsigned int q = 0; q < velocity.n_q_points; ++q)
+ {
+ Tensor<2, dim, vector_t> grad_u;
+ if constexpr (dim == 1)
+ grad_u[0] = velocity.get_gradient(q);
+ else
+ grad_u = velocity.get_gradient(q);
+
+ Tensor<1, dim, vector_t> val_u;
+ if constexpr (dim == 1)
+ val_u[0] = velocity.get_value(q);
+ else
+ val_u = velocity.get_value(q);
+
+ vector_t pres = pressure.get_value(q);
+ vector_t div = -trace(grad_u);
+ pressure.submit_value(div, q);
+
+ // subtract p * I
+ for (unsigned int d = 0; d < dim; ++d)
+ grad_u[d][d] -= pres;
+
+ velocity.submit_gradient(grad_u, q);
+ velocity.submit_value(val_u, q);
+ }
+
+ velocity.integrate(EvaluationFlags::gradients |
+ EvaluationFlags::values);
+ velocity.distribute_local_to_global(dst, 0);
+ pressure.integrate(EvaluationFlags::values);
+ pressure.distribute_local_to_global(dst, dim);
+ }
+ }
+
+
+ void
+ vmult(VectorType &dst, const VectorType &src) const
+ {
+ AssertDimension(dst.size(), dim + 1);
+ for (unsigned int d = 0; d < dim + 1; ++d)
+ dst[d] = 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;
+ if constexpr (dim == 1)
+ GridGenerator::hyper_cube(triangulation);
+ else
+ create_mesh(triangulation);
+
+ if (fe_degree == 1)
+ triangulation.refine_global(4 - dim);
+ else
+ triangulation.refine_global(3 - dim);
+
+ FE_Q<dim> fe_u(fe_degree + 1);
+ FE_Q<dim> fe_p(fe_degree);
+ FESystem<dim> fe(fe_u, 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.close();
+
+ BlockSparsityPattern sparsity_pattern;
+ BlockSparseMatrix<double> system_matrix;
+
+ BlockVector<double> solution;
+ BlockVector<double> system_rhs;
+ std::vector<Vector<double>> vec1, vec2;
+
+ dof_handler.distribute_dofs(fe);
+ dof_handler_u.distribute_dofs(fe_u);
+ dof_handler_p.distribute_dofs(fe_p);
+ DoFRenumbering::component_wise(dof_handler);
+
+ const std::vector<types::global_dof_index> dofs_per_block =
+ DoFTools::count_dofs_per_fe_component(dof_handler);
+
+ {
+ BlockDynamicSparsityPattern csp(dim + 1, dim + 1);
+
+ for (unsigned int d = 0; d < dim + 1; ++d)
+ for (unsigned int e = 0; e < dim + 1; ++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);
+
+ solution.reinit(dim + 1);
+ for (unsigned int i = 0; i < dim + 1; ++i)
+ solution.block(i).reinit(dofs_per_block[i]);
+ solution.collect_sizes();
+
+ system_rhs.reinit(solution);
+
+ vec1.resize(dim + 1);
+ vec2.resize(dim + 1);
+ vec1[0].reinit(dofs_per_block[0]);
+ vec2[0].reinit(vec1[0]);
+ for (unsigned int i = 1; i < dim; ++i)
+ {
+ vec1[i].reinit(vec1[0]);
+ vec2[i].reinit(vec1[0]);
+ }
+ vec1[dim].reinit(dofs_per_block[dim]);
+ vec2[dim].reinit(vec1[dim]);
+
+ // this is from step-22
+ {
+ QGauss<dim> quadrature_formula(fe_degree + 2);
+
+ FEValues<dim> fe_values(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<Tensor<2, dim>> phi_grad_u(dofs_per_cell);
+ std::vector<Tensor<1, dim>> phi_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_grad_u[k] = fe_values[velocities].gradient(k, q);
+ phi_u[k] = fe_values[velocities].value(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_u[i] * phi_u[j] +
+ scalar_product(phi_grad_u[i], phi_grad_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);
+ }
+ }
+
+ // first system_rhs with random numbers
+ for (unsigned int i = 0; i < dim + 1; ++i)
+ for (unsigned int j = 0; j < system_rhs.block(i).size(); ++j)
+ {
+ const double val = -1. + 2. * random_value<double>();
+ system_rhs.block(i)(j) = val;
+ vec1[i](j) = val;
+ }
+
+ // setup matrix-free structure
+ {
+ std::vector<const DoFHandler<dim> *> dofs;
+ dofs.push_back(&dof_handler_u);
+ dofs.push_back(&dof_handler_p);
+ AffineConstraints<double> dummy_constraints;
+ dummy_constraints.close();
+ std::vector<const AffineConstraints<double> *> constraints;
+ constraints.push_back(&dummy_constraints);
+ constraints.push_back(&dummy_constraints);
+ QGauss<1> quad(fe_degree + 2);
+ mf_data.reinit(MappingQ1<dim>{},
+ dofs,
+ constraints,
+ quad,
+ typename MatrixFree<dim>::AdditionalData(
+ MatrixFree<dim>::AdditionalData::none));
+ }
+
+ system_matrix.vmult(solution, system_rhs);
+
+ using VectorType = std::vector<Vector<double>>;
+ MatrixFreeTest<dim, fe_degree, VectorType> mf(mf_data);
+ mf.vmult(vec2, vec1);
+
+ // Verification
+ double error = 0.;
+ for (unsigned int i = 0; i < dim + 1; ++i)
+ for (unsigned int j = 0; j < system_rhs.block(i).size(); ++j)
+ error += std::fabs(solution.block(i)(j) - vec2[i](j));
+ double relative = solution.block(0).l1_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("1d");
+ test<1, 1>();
+ deallog.pop();
+ deallog.push("2d");
+ test<2, 1>();
+ deallog.pop();
+ deallog.push("3d");
+ test<3, 1>();
+ deallog.pop();
+ }
+}
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