]> https://gitweb.dealii.org/ - dealii.git/commitdiff
New test case
authorMartin Kronbichler <martin.kronbichler@rub.de>
Tue, 26 Mar 2024 16:40:05 +0000 (17:40 +0100)
committerMartin Kronbichler <martin.kronbichler@rub.de>
Wed, 27 Mar 2024 14:12:11 +0000 (15:12 +0100)
tests/matrix_free/matrix_vector_stokes_1d.cc [new file with mode: 0644]
tests/matrix_free/matrix_vector_stokes_1d.output [new file with mode: 0644]

diff --git a/tests/matrix_free/matrix_vector_stokes_1d.cc b/tests/matrix_free/matrix_vector_stokes_1d.cc
new file mode 100644 (file)
index 0000000..de6274e
--- /dev/null
@@ -0,0 +1,343 @@
+// ------------------------------------------------------------------------
+//
+// 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();
+  }
+}
diff --git a/tests/matrix_free/matrix_vector_stokes_1d.output b/tests/matrix_free/matrix_vector_stokes_1d.output
new file mode 100644 (file)
index 0000000..37c9d6e
--- /dev/null
@@ -0,0 +1,10 @@
+
+DEAL::
+DEAL::Test with doubles
+DEAL::
+DEAL:1d::  Verification fe degree 1: 2.89e-16
+DEAL:1d::
+DEAL:2d::  Verification fe degree 1: 1.05e-15
+DEAL:2d::
+DEAL:3d::  Verification fe degree 1: 1.31e-15
+DEAL:3d::

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