--- /dev/null
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2017 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 at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
+
+// Test the correctness of an implementation for the Stokes operator
+// based on MatrixFreeOperators::Base by comparing with a matrix version.
+
+#include "../tests.h"
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/fe/fe_system.h>
+
+#include <deal.II/dofs/dof_renumbering.h>
+
+#include <deal.II/base/multithread_info.h>
+
+#include <deal.II/lac/block_sparse_matrix.h>
+#include <deal.II/lac/la_parallel_block_vector.h>
+#include <deal.II/lac/vector.h>
+
+#include <deal.II/matrix_free/operators.h>
+
+#include <deal.II/grid/grid_generator.h>
+
+using namespace dealii;
+
+template <int dim, int degree_p, typename BlockVectorType>
+class MatrixFreeTest : public MatrixFreeOperators::Base<dim, BlockVectorType>
+{
+public:
+ typedef typename BlockVectorType::value_type Number;
+ typedef typename MatrixFreeOperators::Base<dim, BlockVectorType> Base;
+
+ void compute_diagonal ()
+ {
+ AssertThrow(false, ExcNotImplemented());
+ }
+
+protected:
+
+ void apply_add(BlockVectorType &dst,const BlockVectorType &src) const
+ {
+ Base::data->cell_loop(&MatrixFreeTest::local_apply_cell, this, dst, src);
+ }
+
+ void local_apply_cell(const dealii::MatrixFree<dim, Number> &data,
+ BlockVectorType &dst, const BlockVectorType &src,
+ const std::pair<unsigned int, unsigned int> &cell_range) const
+ {
+ typedef VectorizedArray<Number> vector_t;
+ 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 (false,true,false);
+ pressure.reinit (cell);
+ pressure.read_dof_values (src.block(1));
+ pressure.evaluate (true,false,false);
+
+ 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 (false,true);
+ velocity.distribute_local_to_global (dst.block(0));
+ pressure.integrate (true,false);
+ pressure.distribute_local_to_global (dst.block(1));
+ }
+ }
+};
+
+
+
+template <int dim, int degree>
+void
+test()
+{
+ Triangulation<dim> tria;
+ GridGenerator::hyper_cube(tria);
+ tria.refine_global(1);
+ tria.begin_active()->set_refine_flag();
+ tria.execute_coarsening_and_refinement();
+
+ FE_Q<dim> fe_u_scal (degree + 1);
+ FESystem<dim> fe_u (fe_u_scal, dim);
+ FE_Q<dim> fe_p(degree);
+ FESystem<dim> fe(fe_u_scal, dim, fe_p, 1);
+
+ DoFHandler<dim> dof(tria);
+ DoFHandler<dim> dof_u(tria);
+ DoFHandler<dim> dof_p(tria);
+
+ dof.distribute_dofs(fe);
+ dof_u.distribute_dofs(fe_u);
+ dof_p.distribute_dofs(fe_p);
+
+ std::shared_ptr<MatrixFree<dim, double> > mf_data;
+
+ dof.distribute_dofs(fe);
+ ConstraintMatrix constraints, constraints_u, constraints_p;
+
+ BlockSparsityPattern sparsity_pattern;
+ BlockSparseMatrix<double> system_matrix;
+
+ BlockVector<double> solution;
+ BlockVector<double> system_rhs;
+ LinearAlgebra::distributed::BlockVector<double> mf_system_rhs;
+ LinearAlgebra::distributed::BlockVector<double> mf_solution;
+
+ std::vector<unsigned int> stokes_sub_blocks(dim + 1, 0);
+ stokes_sub_blocks[dim] = 1;
+ DoFRenumbering::component_wise(dof, stokes_sub_blocks);
+
+ DoFTools::make_hanging_node_constraints (dof, constraints);
+ constraints.close();
+ DoFTools::make_hanging_node_constraints (dof_u, constraints_u);
+ constraints_u.close();
+ DoFTools::make_hanging_node_constraints (dof_p, constraints_p);
+ constraints_p.close();
+
+ std::vector<types::global_dof_index> dofs_per_block(2);
+ DoFTools::count_dofs_per_block(dof, dofs_per_block, stokes_sub_blocks);
+ {
+ 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, csp, constraints, false);
+ sparsity_pattern.copy_from(csp);
+ }
+
+ system_matrix.reinit(sparsity_pattern);
+
+ // this is from step-22
+ {
+ QGauss<dim> quadrature_formula(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<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.begin_active(), endc = dof.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 < dofs_per_cell; ++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);
+ }
+ }
+ }
+
+ cell->get_dof_indices(local_dof_indices);
+ constraints.distribute_local_to_global(local_matrix, local_dof_indices, system_matrix);
+ }
+ }
+
+ solution.reinit(2);
+ mf_solution.reinit(2);
+ for (unsigned int d = 0; d < 2; ++d)
+ {
+ solution.block(d).reinit(dofs_per_block[d]);
+ mf_solution.block(d).reinit(dofs_per_block[d]);
+ }
+ solution.collect_sizes();
+ mf_solution.collect_sizes();
+ system_rhs.reinit(solution);
+ mf_system_rhs.reinit(mf_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.*(double)Testing::rand()/double(RAND_MAX);
+ system_rhs.block(0)(j) = val;
+ mf_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.*(double)Testing::rand()/double(RAND_MAX);
+ system_rhs.block(1)(j) = val;
+ mf_system_rhs.block(1)(j) = val;
+ }
+
+ mf_data = std::shared_ptr<MatrixFree<dim, double> >(new MatrixFree<dim, double>());
+ // setup matrix-free structure
+ {
+ std::vector<const DoFHandler<dim>*> dofs;
+ dofs.push_back(&dof_u);
+ dofs.push_back(&dof_p);
+ std::vector<const ConstraintMatrix *> constraints;
+ constraints.push_back (&constraints_u);
+ constraints.push_back (&constraints_p);
+ QGauss<1> quad(degree+2);
+ // no parallelism
+ mf_data->reinit (dofs, constraints, quad,
+ typename MatrixFree<dim>::AdditionalData
+ (MPI_COMM_WORLD,
+ MatrixFree<dim>::AdditionalData::none));
+ }
+ system_matrix.vmult (solution, system_rhs);
+
+ MatrixFreeTest<dim,degree,LinearAlgebra::distributed::BlockVector<double> > mf;
+ mf.initialize (mf_data);
+ mf.vmult (mf_solution, mf_system_rhs);
+
+ // Verification
+ for (unsigned int i=0; i<mf_solution.size(); ++i)
+ mf_solution(i) -= solution(i);
+ const double error = mf_solution.linfty_norm();
+ const double relative = solution.linfty_norm();
+ deallog << "Verification fe degree " << degree << ": "
+ << error/relative << std::endl << std::endl;
+}
+
+
+
+int main(int /*argc*/, char ** /*argv*/)
+{
+ initlog();
+ deallog.test_mode();
+ deallog.push("2D");
+ test<2,1>();
+ test<2,2>();
+ deallog.pop();
+ deallog.push("3D");
+ test<3,1>();
+ test<3,2>();
+ deallog.pop();
+
+ return 0;
+}
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