From: Daniel Arndt <arndtd@ornl.gov>
Date: Mon, 20 Sep 2021 14:28:53 +0000 (-0400)
Subject: Add test
X-Git-Tag: v9.4.0-rc1~973^2
X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=a6be5e78cb2a3e962fa6b75f535c941167967884;p=dealii.git

Add test
---

diff --git a/tests/lac/block_matrices_06.cc b/tests/lac/block_matrices_06.cc
new file mode 100644
index 0000000000..92916f5ee6
--- /dev/null
+++ b/tests/lac/block_matrices_06.cc
@@ -0,0 +1,480 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2000 - 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.
+//
+// ---------------------------------------------------------------------
+
+// Like lac/block_matrices_04 but for complex numbers
+
+#include <deal.II/base/function.h>
+#include <deal.II/base/quadrature_lib.h>
+
+#include <deal.II/dofs/dof_accessor.h>
+#include <deal.II/dofs/dof_handler.h>
+#include <deal.II/dofs/dof_tools.h>
+
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/fe/fe_values.h>
+#include <deal.II/fe/mapping_q1.h>
+
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/tria.h>
+#include <deal.II/grid/tria_accessor.h>
+#include <deal.II/grid/tria_iterator.h>
+
+#include <deal.II/lac/block_sparse_matrix.h>
+#include <deal.II/lac/block_vector.h>
+#include <deal.II/lac/full_matrix.h>
+#include <deal.II/lac/precondition.h>
+#include <deal.II/lac/solver_cg.h>
+#include <deal.II/lac/sparse_matrix.h>
+#include <deal.II/lac/vector.h>
+#include <deal.II/lac/vector_memory.h>
+
+#include <deal.II/numerics/data_out.h>
+#include <deal.II/numerics/matrix_tools.h>
+#include <deal.II/numerics/vector_tools.h>
+
+#include "../tests.h"
+
+
+template <typename VectorType, class Matrix, class Sparsity>
+class LaplaceProblem
+{
+public:
+  LaplaceProblem(const unsigned int n_blocks);
+
+  void
+  run();
+  void
+  reinit_sparsity();
+  void
+  reinit_vectors();
+
+  VectorType solution;
+
+private:
+  void
+  make_grid_and_dofs();
+  void
+  assemble_system();
+  void
+  solve();
+
+  const unsigned int n_blocks;
+
+  Triangulation<2> triangulation;
+  FE_Q<2>          fe;
+  DoFHandler<2>    dof_handler;
+
+  Sparsity sparsity_pattern;
+  Matrix   system_matrix;
+
+  VectorType system_rhs;
+};
+
+
+template <typename VectorType, class Matrix, class Sparsity>
+LaplaceProblem<VectorType, Matrix, Sparsity>::LaplaceProblem(
+  const unsigned int n_blocks)
+  : n_blocks(n_blocks)
+  , fe(1)
+  , dof_handler(triangulation)
+{
+  sparsity_pattern.reinit(n_blocks, n_blocks);
+}
+
+
+
+template <>
+LaplaceProblem<Vector<std::complex<double>>,
+               SparseMatrix<std::complex<double>>,
+               SparsityPattern>::LaplaceProblem(const unsigned int n_blocks)
+  : n_blocks(n_blocks)
+  , fe(1)
+  , dof_handler(triangulation)
+{}
+
+
+
+template <>
+LaplaceProblem<Vector<std::complex<float>>,
+               SparseMatrix<std::complex<float>>,
+               SparsityPattern>::LaplaceProblem(const unsigned int n_blocks)
+  : n_blocks(n_blocks)
+  , fe(1)
+  , dof_handler(triangulation)
+{}
+
+
+
+template <typename VectorType, class Matrix, class Sparsity>
+void
+LaplaceProblem<VectorType, Matrix, Sparsity>::make_grid_and_dofs()
+{
+  GridGenerator::hyper_cube(triangulation, -1, 1);
+  triangulation.refine_global(3);
+  deallog << "Number of active cells: " << triangulation.n_active_cells()
+          << std::endl;
+  deallog << "Total number of cells: " << triangulation.n_cells() << std::endl;
+
+  dof_handler.distribute_dofs(fe);
+
+  deallog << "Number of degrees of freedom: " << dof_handler.n_dofs()
+          << std::endl;
+
+  reinit_sparsity();
+  DoFTools::make_sparsity_pattern(dof_handler, sparsity_pattern);
+  sparsity_pattern.compress();
+
+  system_matrix.reinit(sparsity_pattern);
+  reinit_vectors();
+}
+
+
+template <>
+void
+LaplaceProblem<Vector<std::complex<double>>,
+               SparseMatrix<std::complex<double>>,
+               SparsityPattern>::reinit_sparsity()
+{
+  sparsity_pattern.reinit(dof_handler.n_dofs(),
+                          dof_handler.n_dofs(),
+                          dof_handler.max_couplings_between_dofs());
+}
+
+
+
+template <>
+void
+LaplaceProblem<Vector<std::complex<double>>,
+               SparseMatrix<std::complex<double>>,
+               SparsityPattern>::reinit_vectors()
+{
+  solution.reinit(dof_handler.n_dofs());
+  system_rhs.reinit(dof_handler.n_dofs());
+}
+
+
+
+template <>
+void
+LaplaceProblem<Vector<std::complex<float>>,
+               SparseMatrix<std::complex<float>>,
+               SparsityPattern>::reinit_sparsity()
+{
+  sparsity_pattern.reinit(dof_handler.n_dofs(),
+                          dof_handler.n_dofs(),
+                          dof_handler.max_couplings_between_dofs());
+}
+
+
+
+template <>
+void
+LaplaceProblem<Vector<std::complex<float>>,
+               SparseMatrix<std::complex<float>>,
+               SparsityPattern>::reinit_vectors()
+{
+  solution.reinit(dof_handler.n_dofs());
+  system_rhs.reinit(dof_handler.n_dofs());
+}
+
+
+
+template <>
+void
+LaplaceProblem<BlockVector<std::complex<double>>,
+               BlockSparseMatrix<std::complex<double>>,
+               BlockSparsityPattern>::reinit_sparsity()
+{
+  switch (n_blocks)
+    {
+      case 2:
+        {
+          const types::global_dof_index n_dofs        = dof_handler.n_dofs();
+          const types::global_dof_index block_size[2] = {n_dofs / 3,
+                                                         n_dofs - n_dofs / 3};
+
+          for (unsigned int i = 0; i < 2; ++i)
+            for (unsigned int j = 0; j < 2; ++j)
+              sparsity_pattern.block(i, j).reinit(
+                block_size[i],
+                block_size[j],
+                dof_handler.max_couplings_between_dofs());
+          sparsity_pattern.collect_sizes();
+
+          break;
+        };
+
+      case 3:
+        {
+          const types::global_dof_index n_dofs        = dof_handler.n_dofs();
+          const types::global_dof_index block_size[3] = {
+            n_dofs / 5, n_dofs / 7, n_dofs - n_dofs / 5 - n_dofs / 7};
+
+          for (unsigned int i = 0; i < 3; ++i)
+            for (unsigned int j = 0; j < 3; ++j)
+              sparsity_pattern.block(i, j).reinit(
+                block_size[i],
+                block_size[j],
+                dof_handler.max_couplings_between_dofs());
+          sparsity_pattern.collect_sizes();
+
+          break;
+        };
+
+      default:
+        AssertThrow(false, ExcNotImplemented());
+    };
+}
+
+
+
+template <>
+void
+LaplaceProblem<BlockVector<std::complex<double>>,
+               BlockSparseMatrix<std::complex<double>>,
+               BlockSparsityPattern>::reinit_vectors()
+{
+  switch (n_blocks)
+    {
+      case 2:
+        {
+          const types::global_dof_index n_dofs         = dof_handler.n_dofs();
+          const types::global_dof_index block_size_[2] = {n_dofs / 3,
+                                                          n_dofs - n_dofs / 3};
+          const std::vector<types::global_dof_index> block_size(
+            &block_size_[0], &block_size_[2]);
+
+          solution.reinit(block_size);
+          system_rhs.reinit(block_size);
+
+          break;
+        };
+
+      case 3:
+        {
+          const types::global_dof_index n_dofs         = dof_handler.n_dofs();
+          const types::global_dof_index block_size_[3] = {
+            n_dofs / 5, n_dofs / 7, n_dofs - n_dofs / 5 - n_dofs / 7};
+          const std::vector<types::global_dof_index> block_size(
+            &block_size_[0], &block_size_[3]);
+
+          solution.reinit(block_size);
+          system_rhs.reinit(block_size);
+
+          break;
+        };
+
+      default:
+        AssertThrow(false, ExcNotImplemented());
+    };
+}
+
+
+
+template <typename VectorType, class Matrix, class Sparsity>
+void
+LaplaceProblem<VectorType, Matrix, Sparsity>::assemble_system()
+{
+  QGauss<2>   quadrature_formula(2);
+  FEValues<2> fe_values(fe,
+                        quadrature_formula,
+                        UpdateFlags(update_values | update_gradients |
+                                    update_JxW_values));
+
+  const unsigned int dofs_per_cell = fe.dofs_per_cell;
+  const unsigned int n_q_points    = quadrature_formula.size();
+
+  FullMatrix<typename Matrix::value_type>   cell_matrix(dofs_per_cell,
+                                                      dofs_per_cell);
+  ::Vector<typename VectorType::value_type> cell_rhs(dofs_per_cell);
+
+  std::vector<types::global_dof_index> local_dof_indices(dofs_per_cell);
+
+  DoFHandler<2>::active_cell_iterator cell = dof_handler.begin_active(),
+                                      endc = dof_handler.end();
+  for (; cell != endc; ++cell)
+    {
+      fe_values.reinit(cell);
+
+      cell_matrix = 0;
+      cell_rhs    = 0;
+
+      for (unsigned int i = 0; i < dofs_per_cell; ++i)
+        for (unsigned int j = 0; j < dofs_per_cell; ++j)
+          for (unsigned int q_point = 0; q_point < n_q_points; ++q_point)
+            cell_matrix(i, j) +=
+              (fe_values.shape_grad(i, q_point) *
+               fe_values.shape_grad(j, q_point) * fe_values.JxW(q_point));
+
+      for (unsigned int i = 0; i < dofs_per_cell; ++i)
+        for (unsigned int q_point = 0; q_point < n_q_points; ++q_point)
+          cell_rhs(i) +=
+            (fe_values.shape_value(i, q_point) * 1 * fe_values.JxW(q_point));
+
+      cell->get_dof_indices(local_dof_indices);
+
+      for (unsigned int i = 0; i < dofs_per_cell; ++i)
+        for (unsigned int j = 0; j < dofs_per_cell; ++j)
+          system_matrix.add(local_dof_indices[i],
+                            local_dof_indices[j],
+                            cell_matrix(i, j));
+
+      for (unsigned int i = 0; i < dofs_per_cell; ++i)
+        system_rhs(local_dof_indices[i]) += cell_rhs(i);
+    };
+
+
+  std::map<types::global_dof_index, typename VectorType::value_type>
+    boundary_values;
+  VectorTools::interpolate_boundary_values(
+    dof_handler,
+    0,
+    Functions::ZeroFunction<2, typename VectorType::value_type>(),
+    boundary_values);
+  MatrixTools::apply_boundary_values(boundary_values,
+                                     system_matrix,
+                                     solution,
+                                     system_rhs);
+}
+
+
+template <typename VectorType, class Matrix, class Sparsity>
+void
+LaplaceProblem<VectorType, Matrix, Sparsity>::solve()
+{
+  SolverControl                     solver_control(1000, 1e-12, false, false);
+  PrimitiveVectorMemory<VectorType> vector_memory;
+  SolverCG<VectorType>              cg(solver_control, vector_memory);
+
+  PreconditionJacobi<Matrix> preconditioner;
+  preconditioner.initialize(system_matrix, 0.8);
+
+  cg.solve(system_matrix, solution, system_rhs, preconditioner);
+}
+
+
+template <typename VectorType, class Matrix, class Sparsity>
+void
+LaplaceProblem<VectorType, Matrix, Sparsity>::run()
+{
+  make_grid_and_dofs();
+  assemble_system();
+  solve();
+
+  for (unsigned int i = 0; i < solution.size(); ++i)
+    deallog
+      //<< typeid(VectorType).name ()
+      //<< ' '
+      //<< typeid(Matrix).name ()
+      //<< '-'
+      << i << ' ' << solution(i) << std::endl;
+}
+
+
+
+int
+main()
+{
+  initlog();
+  deallog << std::setprecision(2);
+
+
+  // vector of solution vectors
+  std::vector<std::vector<std::complex<double>>> solutions;
+
+  if (true)
+    {
+      LaplaceProblem<Vector<std::complex<double>>,
+                     SparseMatrix<std::complex<double>>,
+                     SparsityPattern>
+        laplace_problem(2);
+      laplace_problem.run();
+
+      solutions.push_back(std::vector<std::complex<double>>());
+      solutions.back().resize(laplace_problem.solution.size());
+      for (unsigned int i = 0; i < laplace_problem.solution.size(); ++i)
+        solutions.back()[i] = laplace_problem.solution(i);
+    };
+
+  if (true)
+    {
+      LaplaceProblem<Vector<std::complex<float>>,
+                     SparseMatrix<std::complex<float>>,
+                     SparsityPattern>
+        laplace_problem(3);
+      laplace_problem.run();
+
+      solutions.push_back(std::vector<std::complex<double>>());
+      solutions.back().resize(laplace_problem.solution.size());
+      for (unsigned int i = 0; i < laplace_problem.solution.size(); ++i)
+        solutions.back()[i] = laplace_problem.solution(i);
+    };
+
+  if (true)
+    {
+      LaplaceProblem<BlockVector<std::complex<double>>,
+                     BlockSparseMatrix<std::complex<double>>,
+                     BlockSparsityPattern>
+        laplace_problem(2);
+      laplace_problem.run();
+
+      solutions.push_back(std::vector<std::complex<double>>());
+      solutions.back().resize(laplace_problem.solution.size());
+      for (unsigned int i = 0; i < laplace_problem.solution.size(); ++i)
+        solutions.back()[i] = laplace_problem.solution(i);
+    };
+
+  if (true)
+    {
+      LaplaceProblem<BlockVector<std::complex<double>>,
+                     BlockSparseMatrix<std::complex<double>>,
+                     BlockSparsityPattern>
+        laplace_problem(3);
+      laplace_problem.run();
+
+      solutions.push_back(std::vector<std::complex<double>>());
+      solutions.back().resize(laplace_problem.solution.size());
+      for (unsigned int i = 0; i < laplace_problem.solution.size(); ++i)
+        solutions.back()[i] = laplace_problem.solution(i);
+    };
+
+  const unsigned int n_datasets = solutions.size();
+  deallog << "Checking " << n_datasets << " data sets." << std::endl;
+
+  for (unsigned int i = 1; i < n_datasets; ++i)
+    Assert(solutions[i].size() == solutions[i].size(), ExcInternalError());
+
+  deallog << std::setprecision(16);
+  for (unsigned int i = 1; i < n_datasets; ++i)
+    {
+      // relative accuracy. data set 1 is computed using floats
+      // instead of doubles, so lower our requirements
+      const double accuracy = (i == 1 ? 1e-6 : 1e-12);
+
+      for (unsigned int j = 0; j < solutions[0].size(); ++j)
+        if (std::abs(solutions[i][j] - solutions[0][j]) >
+            accuracy * std::abs(solutions[i][j] + solutions[0][j]))
+          {
+            deallog << "Discrepancy: i=" << i << ", j=" << j
+                    << ", sol[i][j]=" << solutions[i][j]
+                    << ", sol[0][j]=" << solutions[0][j] << std::endl;
+            deallog << std::flush;
+            Assert(false, ExcInternalError());
+          };
+    };
+
+
+  return 0;
+}
diff --git a/tests/lac/block_matrices_06.with_complex_values=on.output b/tests/lac/block_matrices_06.with_complex_values=on.output
new file mode 100644
index 0000000000..46a1add110
--- /dev/null
+++ b/tests/lac/block_matrices_06.with_complex_values=on.output
@@ -0,0 +1,338 @@
+
+DEAL::Number of active cells: 64
+DEAL::Total number of cells: 85
+DEAL::Number of degrees of freedom: 81
+DEAL::0 (0.0,0.0)
+DEAL::1 (0.0,0.0)
+DEAL::2 (0.0,0.0)
+DEAL::3 (0.075,0.0)
+DEAL::4 (0.0,0.0)
+DEAL::5 (0.11,0.0)
+DEAL::6 (0.0,0.0)
+DEAL::7 (0.11,0.0)
+DEAL::8 (0.18,0.0)
+DEAL::9 (0.0,0.0)
+DEAL::10 (0.14,0.0)
+DEAL::11 (0.0,0.0)
+DEAL::12 (0.14,0.0)
+DEAL::13 (0.22,0.0)
+DEAL::14 (0.23,0.0)
+DEAL::15 (0.0,0.0)
+DEAL::16 (0.14,0.0)
+DEAL::17 (0.22,0.0)
+DEAL::18 (0.0,0.0)
+DEAL::19 (0.14,0.0)
+DEAL::20 (0.23,0.0)
+DEAL::21 (0.27,0.0)
+DEAL::22 (0.28,0.0)
+DEAL::23 (0.28,0.0)
+DEAL::24 (0.30,0.0)
+DEAL::25 (0.0,0.0)
+DEAL::26 (0.14,0.0)
+DEAL::27 (0.0,0.0)
+DEAL::28 (0.11,0.0)
+DEAL::29 (0.22,0.0)
+DEAL::30 (0.18,0.0)
+DEAL::31 (0.0,0.0)
+DEAL::32 (0.075,0.0)
+DEAL::33 (0.0,0.0)
+DEAL::34 (0.0,0.0)
+DEAL::35 (0.11,0.0)
+DEAL::36 (0.0,0.0)
+DEAL::37 (0.27,0.0)
+DEAL::38 (0.22,0.0)
+DEAL::39 (0.28,0.0)
+DEAL::40 (0.23,0.0)
+DEAL::41 (0.14,0.0)
+DEAL::42 (0.0,0.0)
+DEAL::43 (0.14,0.0)
+DEAL::44 (0.0,0.0)
+DEAL::45 (0.0,0.0)
+DEAL::46 (0.14,0.0)
+DEAL::47 (0.22,0.0)
+DEAL::48 (0.0,0.0)
+DEAL::49 (0.11,0.0)
+DEAL::50 (0.18,0.0)
+DEAL::51 (0.27,0.0)
+DEAL::52 (0.28,0.0)
+DEAL::53 (0.22,0.0)
+DEAL::54 (0.23,0.0)
+DEAL::55 (0.0,0.0)
+DEAL::56 (0.075,0.0)
+DEAL::57 (0.11,0.0)
+DEAL::58 (0.0,0.0)
+DEAL::59 (0.0,0.0)
+DEAL::60 (0.0,0.0)
+DEAL::61 (0.14,0.0)
+DEAL::62 (0.14,0.0)
+DEAL::63 (0.0,0.0)
+DEAL::64 (0.0,0.0)
+DEAL::65 (0.27,0.0)
+DEAL::66 (0.22,0.0)
+DEAL::67 (0.22,0.0)
+DEAL::68 (0.18,0.0)
+DEAL::69 (0.14,0.0)
+DEAL::70 (0.0,0.0)
+DEAL::71 (0.11,0.0)
+DEAL::72 (0.0,0.0)
+DEAL::73 (0.14,0.0)
+DEAL::74 (0.11,0.0)
+DEAL::75 (0.0,0.0)
+DEAL::76 (0.0,0.0)
+DEAL::77 (0.075,0.0)
+DEAL::78 (0.0,0.0)
+DEAL::79 (0.0,0.0)
+DEAL::80 (0.0,0.0)
+DEAL::Number of active cells: 64
+DEAL::Total number of cells: 85
+DEAL::Number of degrees of freedom: 81
+DEAL::0 (0.0,0.0)
+DEAL::1 (0.0,0.0)
+DEAL::2 (0.0,0.0)
+DEAL::3 (0.075,0.0)
+DEAL::4 (0.0,0.0)
+DEAL::5 (0.11,0.0)
+DEAL::6 (0.0,0.0)
+DEAL::7 (0.11,0.0)
+DEAL::8 (0.18,0.0)
+DEAL::9 (0.0,0.0)
+DEAL::10 (0.14,0.0)
+DEAL::11 (0.0,0.0)
+DEAL::12 (0.14,0.0)
+DEAL::13 (0.22,0.0)
+DEAL::14 (0.23,0.0)
+DEAL::15 (0.0,0.0)
+DEAL::16 (0.14,0.0)
+DEAL::17 (0.22,0.0)
+DEAL::18 (0.0,0.0)
+DEAL::19 (0.14,0.0)
+DEAL::20 (0.23,0.0)
+DEAL::21 (0.27,0.0)
+DEAL::22 (0.28,0.0)
+DEAL::23 (0.28,0.0)
+DEAL::24 (0.30,0.0)
+DEAL::25 (0.0,0.0)
+DEAL::26 (0.14,0.0)
+DEAL::27 (0.0,0.0)
+DEAL::28 (0.11,0.0)
+DEAL::29 (0.22,0.0)
+DEAL::30 (0.18,0.0)
+DEAL::31 (0.0,0.0)
+DEAL::32 (0.075,0.0)
+DEAL::33 (0.0,0.0)
+DEAL::34 (0.0,0.0)
+DEAL::35 (0.11,0.0)
+DEAL::36 (0.0,0.0)
+DEAL::37 (0.27,0.0)
+DEAL::38 (0.22,0.0)
+DEAL::39 (0.28,0.0)
+DEAL::40 (0.23,0.0)
+DEAL::41 (0.14,0.0)
+DEAL::42 (0.0,0.0)
+DEAL::43 (0.14,0.0)
+DEAL::44 (0.0,0.0)
+DEAL::45 (0.0,0.0)
+DEAL::46 (0.14,0.0)
+DEAL::47 (0.22,0.0)
+DEAL::48 (0.0,0.0)
+DEAL::49 (0.11,0.0)
+DEAL::50 (0.18,0.0)
+DEAL::51 (0.27,0.0)
+DEAL::52 (0.28,0.0)
+DEAL::53 (0.22,0.0)
+DEAL::54 (0.23,0.0)
+DEAL::55 (0.0,0.0)
+DEAL::56 (0.075,0.0)
+DEAL::57 (0.11,0.0)
+DEAL::58 (0.0,0.0)
+DEAL::59 (0.0,0.0)
+DEAL::60 (0.0,0.0)
+DEAL::61 (0.14,0.0)
+DEAL::62 (0.14,0.0)
+DEAL::63 (0.0,0.0)
+DEAL::64 (0.0,0.0)
+DEAL::65 (0.27,0.0)
+DEAL::66 (0.22,0.0)
+DEAL::67 (0.22,0.0)
+DEAL::68 (0.18,0.0)
+DEAL::69 (0.14,0.0)
+DEAL::70 (0.0,0.0)
+DEAL::71 (0.11,0.0)
+DEAL::72 (0.0,0.0)
+DEAL::73 (0.14,0.0)
+DEAL::74 (0.11,0.0)
+DEAL::75 (0.0,0.0)
+DEAL::76 (0.0,0.0)
+DEAL::77 (0.075,0.0)
+DEAL::78 (0.0,0.0)
+DEAL::79 (0.0,0.0)
+DEAL::80 (0.0,0.0)
+DEAL::Number of active cells: 64
+DEAL::Total number of cells: 85
+DEAL::Number of degrees of freedom: 81
+DEAL::0 (0.0,0.0)
+DEAL::1 (0.0,0.0)
+DEAL::2 (0.0,0.0)
+DEAL::3 (0.075,0.0)
+DEAL::4 (0.0,0.0)
+DEAL::5 (0.11,0.0)
+DEAL::6 (0.0,0.0)
+DEAL::7 (0.11,0.0)
+DEAL::8 (0.18,0.0)
+DEAL::9 (0.0,0.0)
+DEAL::10 (0.14,0.0)
+DEAL::11 (0.0,0.0)
+DEAL::12 (0.14,0.0)
+DEAL::13 (0.22,0.0)
+DEAL::14 (0.23,0.0)
+DEAL::15 (0.0,0.0)
+DEAL::16 (0.14,0.0)
+DEAL::17 (0.22,0.0)
+DEAL::18 (0.0,0.0)
+DEAL::19 (0.14,0.0)
+DEAL::20 (0.23,0.0)
+DEAL::21 (0.27,0.0)
+DEAL::22 (0.28,0.0)
+DEAL::23 (0.28,0.0)
+DEAL::24 (0.30,0.0)
+DEAL::25 (0.0,0.0)
+DEAL::26 (0.14,0.0)
+DEAL::27 (0.0,0.0)
+DEAL::28 (0.11,0.0)
+DEAL::29 (0.22,0.0)
+DEAL::30 (0.18,0.0)
+DEAL::31 (0.0,0.0)
+DEAL::32 (0.075,0.0)
+DEAL::33 (0.0,0.0)
+DEAL::34 (0.0,0.0)
+DEAL::35 (0.11,0.0)
+DEAL::36 (0.0,0.0)
+DEAL::37 (0.27,0.0)
+DEAL::38 (0.22,0.0)
+DEAL::39 (0.28,0.0)
+DEAL::40 (0.23,0.0)
+DEAL::41 (0.14,0.0)
+DEAL::42 (0.0,0.0)
+DEAL::43 (0.14,0.0)
+DEAL::44 (0.0,0.0)
+DEAL::45 (0.0,0.0)
+DEAL::46 (0.14,0.0)
+DEAL::47 (0.22,0.0)
+DEAL::48 (0.0,0.0)
+DEAL::49 (0.11,0.0)
+DEAL::50 (0.18,0.0)
+DEAL::51 (0.27,0.0)
+DEAL::52 (0.28,0.0)
+DEAL::53 (0.22,0.0)
+DEAL::54 (0.23,0.0)
+DEAL::55 (0.0,0.0)
+DEAL::56 (0.075,0.0)
+DEAL::57 (0.11,0.0)
+DEAL::58 (0.0,0.0)
+DEAL::59 (0.0,0.0)
+DEAL::60 (0.0,0.0)
+DEAL::61 (0.14,0.0)
+DEAL::62 (0.14,0.0)
+DEAL::63 (0.0,0.0)
+DEAL::64 (0.0,0.0)
+DEAL::65 (0.27,0.0)
+DEAL::66 (0.22,0.0)
+DEAL::67 (0.22,0.0)
+DEAL::68 (0.18,0.0)
+DEAL::69 (0.14,0.0)
+DEAL::70 (0.0,0.0)
+DEAL::71 (0.11,0.0)
+DEAL::72 (0.0,0.0)
+DEAL::73 (0.14,0.0)
+DEAL::74 (0.11,0.0)
+DEAL::75 (0.0,0.0)
+DEAL::76 (0.0,0.0)
+DEAL::77 (0.075,0.0)
+DEAL::78 (0.0,0.0)
+DEAL::79 (0.0,0.0)
+DEAL::80 (0.0,0.0)
+DEAL::Number of active cells: 64
+DEAL::Total number of cells: 85
+DEAL::Number of degrees of freedom: 81
+DEAL::0 (0.0,0.0)
+DEAL::1 (0.0,0.0)
+DEAL::2 (0.0,0.0)
+DEAL::3 (0.075,0.0)
+DEAL::4 (0.0,0.0)
+DEAL::5 (0.11,0.0)
+DEAL::6 (0.0,0.0)
+DEAL::7 (0.11,0.0)
+DEAL::8 (0.18,0.0)
+DEAL::9 (0.0,0.0)
+DEAL::10 (0.14,0.0)
+DEAL::11 (0.0,0.0)
+DEAL::12 (0.14,0.0)
+DEAL::13 (0.22,0.0)
+DEAL::14 (0.23,0.0)
+DEAL::15 (0.0,0.0)
+DEAL::16 (0.14,0.0)
+DEAL::17 (0.22,0.0)
+DEAL::18 (0.0,0.0)
+DEAL::19 (0.14,0.0)
+DEAL::20 (0.23,0.0)
+DEAL::21 (0.27,0.0)
+DEAL::22 (0.28,0.0)
+DEAL::23 (0.28,0.0)
+DEAL::24 (0.30,0.0)
+DEAL::25 (0.0,0.0)
+DEAL::26 (0.14,0.0)
+DEAL::27 (0.0,0.0)
+DEAL::28 (0.11,0.0)
+DEAL::29 (0.22,0.0)
+DEAL::30 (0.18,0.0)
+DEAL::31 (0.0,0.0)
+DEAL::32 (0.075,0.0)
+DEAL::33 (0.0,0.0)
+DEAL::34 (0.0,0.0)
+DEAL::35 (0.11,0.0)
+DEAL::36 (0.0,0.0)
+DEAL::37 (0.27,0.0)
+DEAL::38 (0.22,0.0)
+DEAL::39 (0.28,0.0)
+DEAL::40 (0.23,0.0)
+DEAL::41 (0.14,0.0)
+DEAL::42 (0.0,0.0)
+DEAL::43 (0.14,0.0)
+DEAL::44 (0.0,0.0)
+DEAL::45 (0.0,0.0)
+DEAL::46 (0.14,0.0)
+DEAL::47 (0.22,0.0)
+DEAL::48 (0.0,0.0)
+DEAL::49 (0.11,0.0)
+DEAL::50 (0.18,0.0)
+DEAL::51 (0.27,0.0)
+DEAL::52 (0.28,0.0)
+DEAL::53 (0.22,0.0)
+DEAL::54 (0.23,0.0)
+DEAL::55 (0.0,0.0)
+DEAL::56 (0.075,0.0)
+DEAL::57 (0.11,0.0)
+DEAL::58 (0.0,0.0)
+DEAL::59 (0.0,0.0)
+DEAL::60 (0.0,0.0)
+DEAL::61 (0.14,0.0)
+DEAL::62 (0.14,0.0)
+DEAL::63 (0.0,0.0)
+DEAL::64 (0.0,0.0)
+DEAL::65 (0.27,0.0)
+DEAL::66 (0.22,0.0)
+DEAL::67 (0.22,0.0)
+DEAL::68 (0.18,0.0)
+DEAL::69 (0.14,0.0)
+DEAL::70 (0.0,0.0)
+DEAL::71 (0.11,0.0)
+DEAL::72 (0.0,0.0)
+DEAL::73 (0.14,0.0)
+DEAL::74 (0.11,0.0)
+DEAL::75 (0.0,0.0)
+DEAL::76 (0.0,0.0)
+DEAL::77 (0.075,0.0)
+DEAL::78 (0.0,0.0)
+DEAL::79 (0.0,0.0)
+DEAL::80 (0.0,0.0)
+DEAL::Checking 4 data sets.