]> https://gitweb.dealii.org/ - dealii-svn.git/commitdiff
copy step 16
authorkanschat <kanschat@0785d39b-7218-0410-832d-ea1e28bc413d>
Wed, 21 Aug 2013 19:13:29 +0000 (19:13 +0000)
committerkanschat <kanschat@0785d39b-7218-0410-832d-ea1e28bc413d>
Wed, 21 Aug 2013 19:13:29 +0000 (19:13 +0000)
git-svn-id: https://svn.dealii.org/trunk@30381 0785d39b-7218-0410-832d-ea1e28bc413d

tests/multigrid/step-16-02.cc [new file with mode: 0644]
tests/multigrid/step-16-02/cmp/generic [new file with mode: 0644]

diff --git a/tests/multigrid/step-16-02.cc b/tests/multigrid/step-16-02.cc
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+// ---------------------------------------------------------------------
+// $Id$
+//
+// Copyright (C) 2003 - 2013 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.
+//
+// ---------------------------------------------------------------------
+
+/*
+ * Authors: Guido Kanschat, University of Heidelberg, 2003
+ *          Baerbel Janssen, University of Heidelberg, 2010
+ *          Wolfgang Bangerth, Texas A&M University, 2010
+ */
+
+#include "../tests.h"
+#include <deal.II/base/logstream.h>
+
+#include <deal.II/base/quadrature_lib.h>
+#include <deal.II/base/function.h>
+#include <deal.II/base/logstream.h>
+#include <deal.II/base/utilities.h>
+
+#include <deal.II/lac/constraint_matrix.h>
+#include <deal.II/lac/vector.h>
+#include <deal.II/lac/full_matrix.h>
+#include <deal.II/lac/sparse_matrix.h>
+#include <deal.II/lac/solver_cg.h>
+#include <deal.II/lac/precondition.h>
+
+#include <deal.II/grid/tria.h>
+#include <deal.II/grid/tria_accessor.h>
+#include <deal.II/grid/tria_iterator.h>
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/grid_refinement.h>
+#include <deal.II/grid/tria_boundary_lib.h>
+
+#include <deal.II/dofs/dof_accessor.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/numerics/vector_tools.h>
+#include <deal.II/numerics/data_out.h>
+#include <deal.II/numerics/error_estimator.h>
+
+#include <deal.II/multigrid/mg_dof_handler.h>
+#include <deal.II/multigrid/multigrid.h>
+#include <deal.II/multigrid/mg_transfer.h>
+#include <deal.II/multigrid/mg_tools.h>
+#include <deal.II/multigrid/mg_coarse.h>
+#include <deal.II/multigrid/mg_smoother.h>
+#include <deal.II/multigrid/mg_matrix.h>
+
+#include <fstream>
+#include <sstream>
+
+using namespace dealii;
+
+template <int dim>
+class LaplaceProblem
+{
+public:
+  LaplaceProblem (const unsigned int deg);
+  void run ();
+
+private:
+  void setup_system ();
+  void assemble_system ();
+  void assemble_multigrid ();
+  void solve ();
+  void refine_grid ();
+  void output_results (const unsigned int cycle) const;
+
+  Triangulation<dim>   triangulation;
+  FE_Q<dim>            fe;
+  MGDoFHandler<dim>    mg_dof_handler;
+
+  SparsityPattern      sparsity_pattern;
+  SparseMatrix<double> system_matrix;
+
+  ConstraintMatrix     hanging_node_constraints;
+  ConstraintMatrix     constraints;
+
+  Vector<double>       solution;
+  Vector<double>       system_rhs;
+
+  const unsigned int degree;
+
+  MGLevelObject<SparsityPattern>       mg_sparsity_patterns;
+  MGLevelObject<SparseMatrix<double> > mg_matrices;
+  MGLevelObject<SparseMatrix<double> > mg_interface_matrices;
+  MGConstrainedDoFs                    mg_constrained_dofs;
+};
+
+
+template <int dim>
+class Coefficient : public Function<dim>
+{
+public:
+  Coefficient () : Function<dim>() {}
+
+  virtual double value (const Point<dim>   &p,
+                        const unsigned int  component = 0) const;
+
+  virtual void value_list (const std::vector<Point<dim> > &points,
+                           std::vector<double>            &values,
+                           const unsigned int              component = 0) const;
+};
+
+
+
+template <int dim>
+double Coefficient<dim>::value (const Point<dim> &p,
+                                const unsigned int) const
+{
+  if (p.square() < 0.5*0.5)
+    return 20;
+  else
+    return 1;
+}
+
+
+
+template <int dim>
+void Coefficient<dim>::value_list (const std::vector<Point<dim> > &points,
+                                   std::vector<double>            &values,
+                                   const unsigned int              component) const
+{
+  const unsigned int n_points = points.size();
+
+  Assert (values.size() == n_points,
+          ExcDimensionMismatch (values.size(), n_points));
+
+  Assert (component == 0,
+          ExcIndexRange (component, 0, 1));
+
+  for (unsigned int i=0; i<n_points; ++i)
+    values[i] = Coefficient<dim>::value (points[i]);
+}
+
+
+template <int dim>
+LaplaceProblem<dim>::LaplaceProblem (const unsigned int degree)
+  :
+  triangulation (Triangulation<dim>::
+                 limit_level_difference_at_vertices),
+  fe (degree),
+  mg_dof_handler (triangulation),
+  degree(degree)
+{}
+
+
+template <int dim>
+void LaplaceProblem<dim>::setup_system ()
+{
+  mg_dof_handler.distribute_dofs (fe);
+  deallog << "Number of degrees of freedom: "
+          << mg_dof_handler.n_dofs();
+
+  for (unsigned int l=0; l<triangulation.n_levels(); ++l)
+    deallog << "   " << 'L' << l << ": "
+            << mg_dof_handler.n_dofs(l);
+  deallog  << std::endl;
+
+  sparsity_pattern.reinit (mg_dof_handler.n_dofs(),
+                           mg_dof_handler.n_dofs(),
+                           mg_dof_handler.max_couplings_between_dofs());
+  DoFTools::make_sparsity_pattern (
+    static_cast<const DoFHandler<dim>&>(mg_dof_handler),
+    sparsity_pattern);
+
+  solution.reinit (mg_dof_handler.n_dofs());
+  system_rhs.reinit (mg_dof_handler.n_dofs());
+
+  constraints.clear ();
+  hanging_node_constraints.clear ();
+  DoFTools::make_hanging_node_constraints (mg_dof_handler, constraints);
+  DoFTools::make_hanging_node_constraints (mg_dof_handler, hanging_node_constraints);
+  typename FunctionMap<dim>::type      dirichlet_boundary;
+  ZeroFunction<dim>                    homogeneous_dirichlet_bc (1);
+  dirichlet_boundary[0] = &homogeneous_dirichlet_bc;
+  MappingQ1<dim> mapping;
+  VectorTools::interpolate_boundary_values (mapping,
+                                            mg_dof_handler,
+                                            dirichlet_boundary,
+                                            constraints);
+  constraints.close ();
+  hanging_node_constraints.close ();
+  constraints.condense (sparsity_pattern);
+  sparsity_pattern.compress();
+  system_matrix.reinit (sparsity_pattern);
+
+  mg_constrained_dofs.clear();
+  mg_constrained_dofs.initialize(mg_dof_handler, dirichlet_boundary);
+  const unsigned int n_levels = triangulation.n_levels();
+
+  mg_interface_matrices.resize(0, n_levels-1);
+  mg_interface_matrices.clear ();
+  mg_matrices.resize(0, n_levels-1);
+  mg_matrices.clear ();
+  mg_sparsity_patterns.resize(0, n_levels-1);
+
+  for (unsigned int level=0; level<n_levels; ++level)
+    {
+      CompressedSparsityPattern csp;
+      csp.reinit(mg_dof_handler.n_dofs(level),
+                 mg_dof_handler.n_dofs(level));
+      MGTools::make_sparsity_pattern(mg_dof_handler, csp, level);
+
+      mg_sparsity_patterns[level].copy_from (csp);
+
+      mg_matrices[level].reinit(mg_sparsity_patterns[level]);
+      mg_interface_matrices[level].reinit(mg_sparsity_patterns[level]);
+    }
+}
+
+
+template <int dim>
+void LaplaceProblem<dim>::assemble_system ()
+{
+  const QGauss<dim>  quadrature_formula(degree+1);
+
+  FEValues<dim> fe_values (fe, quadrature_formula,
+                           update_values    |  update_gradients |
+                           update_quadrature_points  |  update_JxW_values);
+
+  const unsigned int   dofs_per_cell = fe.dofs_per_cell;
+  const unsigned int   n_q_points    = quadrature_formula.size();
+
+  FullMatrix<double>   cell_matrix (dofs_per_cell, dofs_per_cell);
+  Vector<double>       cell_rhs (dofs_per_cell);
+
+  std::vector<types::global_dof_index> local_dof_indices (dofs_per_cell);
+
+  const Coefficient<dim> coefficient;
+  std::vector<double>    coefficient_values (n_q_points);
+
+  typename MGDoFHandler<dim>::active_cell_iterator
+  cell = mg_dof_handler.begin_active(),
+  endc = mg_dof_handler.end();
+  for (; cell!=endc; ++cell)
+    {
+      cell_matrix = 0;
+      cell_rhs = 0;
+
+      fe_values.reinit (cell);
+
+      coefficient.value_list (fe_values.get_quadrature_points(),
+                              coefficient_values);
+
+      for (unsigned int q_point=0; q_point<n_q_points; ++q_point)
+        for (unsigned int i=0; i<dofs_per_cell; ++i)
+          {
+            for (unsigned int j=0; j<dofs_per_cell; ++j)
+              cell_matrix(i,j) += (coefficient_values[q_point] *
+                                   fe_values.shape_grad(i,q_point) *
+                                   fe_values.shape_grad(j,q_point) *
+                                   fe_values.JxW(q_point));
+
+            cell_rhs(i) += (fe_values.shape_value(i,q_point) *
+                            1.0 *
+                            fe_values.JxW(q_point));
+          }
+
+      cell->get_dof_indices (local_dof_indices);
+      constraints.distribute_local_to_global (cell_matrix, cell_rhs,
+                                              local_dof_indices,
+                                              system_matrix, system_rhs);
+    }
+}
+
+
+template <int dim>
+void LaplaceProblem<dim>::assemble_multigrid ()
+{
+  QGauss<dim>  quadrature_formula(1+degree);
+
+  FEValues<dim> fe_values (fe, quadrature_formula,
+                           update_values   | update_gradients |
+                           update_quadrature_points | update_JxW_values);
+
+  const unsigned int   dofs_per_cell   = fe.dofs_per_cell;
+  const unsigned int   n_q_points      = quadrature_formula.size();
+
+  FullMatrix<double>   cell_matrix (dofs_per_cell, dofs_per_cell);
+
+  std::vector<types::global_dof_index> local_dof_indices (dofs_per_cell);
+
+  const Coefficient<dim> coefficient;
+  std::vector<double>    coefficient_values (n_q_points);
+
+  std::vector<std::vector<bool> > interface_dofs
+    = mg_constrained_dofs.get_refinement_edge_indices ();
+  std::vector<std::vector<bool> > boundary_interface_dofs
+    = mg_constrained_dofs.get_refinement_edge_boundary_indices ();
+
+  std::vector<ConstraintMatrix> boundary_constraints (triangulation.n_levels());
+  std::vector<ConstraintMatrix> boundary_interface_constraints (triangulation.n_levels());
+  for (unsigned int level=0; level<triangulation.n_levels(); ++level)
+    {
+      boundary_constraints[level].add_lines (interface_dofs[level]);
+      boundary_constraints[level].add_lines (mg_constrained_dofs.get_boundary_indices()[level]);
+      boundary_constraints[level].close ();
+
+      boundary_interface_constraints[level]
+      .add_lines (boundary_interface_dofs[level]);
+      boundary_interface_constraints[level].close ();
+    }
+
+  typename MGDoFHandler<dim>::cell_iterator cell = mg_dof_handler.begin(),
+                                            endc = mg_dof_handler.end();
+
+  for (; cell!=endc; ++cell)
+    {
+      cell_matrix = 0;
+      fe_values.reinit (cell);
+
+      coefficient.value_list (fe_values.get_quadrature_points(),
+                              coefficient_values);
+
+      for (unsigned int q_point=0; q_point<n_q_points; ++q_point)
+        for (unsigned int i=0; i<dofs_per_cell; ++i)
+          for (unsigned int j=0; j<dofs_per_cell; ++j)
+            cell_matrix(i,j) += (coefficient_values[q_point] *
+                                 fe_values.shape_grad(i,q_point) *
+                                 fe_values.shape_grad(j,q_point) *
+                                 fe_values.JxW(q_point));
+
+      cell->get_mg_dof_indices (local_dof_indices);
+
+      boundary_constraints[cell->level()]
+      .distribute_local_to_global (cell_matrix,
+                                   local_dof_indices,
+                                   mg_matrices[cell->level()]);
+
+      // The next step is again slightly more
+      // obscure (but explained in the @ref
+      // mg_paper): We need the remainder of
+      // the operator that we just copied
+      // into the <code>mg_matrices</code>
+      // object, namely the part on the
+      // interface between cells at the
+      // current level and cells one level
+      // coarser. This matrix exists in two
+      // directions: for interior DoFs (index
+      // $i$) of the current level to those
+      // sitting on the interface (index
+      // $j$), and the other way around. Of
+      // course, since we have a symmetric
+      // operator, one of these matrices is
+      // the transpose of the other.
+      //
+      // The way we assemble these matrices
+      // is as follows: since the are formed
+      // from parts of the local
+      // contributions, we first delete all
+      // those parts of the local
+      // contributions that we are not
+      // interested in, namely all those
+      // elements of the local matrix for
+      // which not $i$ is an interface DoF
+      // and $j$ is not. The result is one of
+      // the two matrices that we are
+      // interested in, and we then copy it
+      // into the
+      // <code>mg_interface_matrices</code>
+      // object. The
+      // <code>boundary_interface_constraints</code>
+      // object at the same time makes sure
+      // that we delete contributions from
+      // all degrees of freedom that are not
+      // only on the interface but also on
+      // the external boundary of the domain.
+      //
+      // The last part to remember is how to
+      // get the other matrix. Since it is
+      // only the transpose, we will later
+      // (in the <code>solve()</code>
+      // function) be able to just pass the
+      // transpose matrix where necessary.
+      for (unsigned int i=0; i<dofs_per_cell; ++i)
+        for (unsigned int j=0; j<dofs_per_cell; ++j)
+          if ( !(interface_dofs[cell->level()][local_dof_indices[i]]==true &&
+                 interface_dofs[cell->level()][local_dof_indices[j]]==false))
+            cell_matrix(i,j) = 0;
+
+      boundary_interface_constraints[cell->level()]
+      .distribute_local_to_global (cell_matrix,
+                                   local_dof_indices,
+                                   mg_interface_matrices[cell->level()]);
+    }
+}
+
+
+
+// @sect4{LaplaceProblem::solve}
+
+// This is the other function that is
+// significantly different in support of the
+// multigrid solver (or, in fact, the
+// preconditioner for which we use the
+// multigrid method).
+//
+// Let us start out by setting up two of the
+// components of multilevel methods: transfer
+// operators between levels, and a solver on
+// the coarsest level. In finite element
+// methods, the transfer operators are
+// derived from the finite element function
+// spaces involved and can often be computed
+// in a generic way independent of the
+// problem under consideration. In that case,
+// we can use the MGTransferPrebuilt class
+// that, given the constraints on the global
+// level and an MGDoFHandler object computes
+// the matrices corresponding to these
+// transfer operators.
+//
+// The second part of the following lines
+// deals with the coarse grid solver. Since
+// our coarse grid is very coarse indeed, we
+// decide for a direct solver (a Householder
+// decomposition of the coarsest level
+// matrix), even if its implementation is not
+// particularly sophisticated. If our coarse
+// mesh had many more cells than the five we
+// have here, something better suited would
+// obviously be necessary here.
+template <int dim>
+void LaplaceProblem<dim>::solve ()
+{
+  MGTransferPrebuilt<Vector<double> > mg_transfer(hanging_node_constraints, mg_constrained_dofs);
+  mg_transfer.build_matrices(mg_dof_handler);
+
+  FullMatrix<double> coarse_matrix;
+  coarse_matrix.copy_from (mg_matrices[0]);
+  MGCoarseGridHouseholder<> coarse_grid_solver;
+  coarse_grid_solver.initialize (coarse_matrix);
+
+  typedef PreconditionSOR<SparseMatrix<double> > Smoother;
+  GrowingVectorMemory<>   vector_memory;
+  MGSmootherRelaxation<SparseMatrix<double>, Smoother, Vector<double> >
+  mg_smoother;
+  mg_smoother.initialize(mg_matrices);
+  mg_smoother.set_steps(2);
+  mg_smoother.set_symmetric(true);
+
+  MGMatrix<> mg_matrix(&mg_matrices);
+  MGMatrix<> mg_interface_up(&mg_interface_matrices);
+  MGMatrix<> mg_interface_down(&mg_interface_matrices);
+
+  Multigrid<Vector<double> > mg(mg_dof_handler,
+                                mg_matrix,
+                                coarse_grid_solver,
+                                mg_transfer,
+                                mg_smoother,
+                                mg_smoother);
+  mg.set_edge_matrices(mg_interface_down, mg_interface_up);
+
+  PreconditionMG<dim, Vector<double>, MGTransferPrebuilt<Vector<double> > >
+  preconditioner(mg_dof_handler, mg, mg_transfer);
+
+  SolverControl solver_control (1000, 1e-12);
+  SolverCG<>    cg (solver_control);
+
+  solution = 0;
+
+  cg.solve (system_matrix, solution, system_rhs,
+            preconditioner);
+  constraints.distribute (solution);
+
+  deallog << "   " << solver_control.last_step()
+          << " CG iterations needed to obtain convergence."
+          << std::endl;
+}
+
+
+
+// @sect4{Postprocessing}
+
+// The following two functions postprocess a
+// solution once it is computed. In
+// particular, the first one refines the mesh
+// at the beginning of each cycle while the
+// second one outputs results at the end of
+// each such cycle. The functions are almost
+// unchanged from those in step-6, with the
+// exception of two minor differences: The
+// KellyErrorEstimator::estimate function
+// wants an argument of type DoFHandler, not
+// MGDoFHandler, and so we have to cast from
+// derived to base class; and we generate
+// output in VTK format, to use the more
+// modern visualization programs available
+// today compared to those that were
+// available when step-6 was written.
+template <int dim>
+void LaplaceProblem<dim>::refine_grid ()
+{
+  Vector<float> estimated_error_per_cell (triangulation.n_active_cells());
+
+  KellyErrorEstimator<dim>::estimate (static_cast<DoFHandler<dim>&>(mg_dof_handler),
+                                      QGauss<dim-1>(3),
+                                      typename FunctionMap<dim>::type(),
+                                      solution,
+                                      estimated_error_per_cell);
+  GridRefinement::refine_and_coarsen_fixed_number (triangulation,
+                                                   estimated_error_per_cell,
+                                                   0.3, 0.03);
+  triangulation.execute_coarsening_and_refinement ();
+}
+
+
+
+template <int dim>
+void LaplaceProblem<dim>::output_results (const unsigned int cycle) const
+{
+  DataOut<dim> data_out;
+
+  data_out.attach_dof_handler (mg_dof_handler);
+  data_out.add_data_vector (solution, "solution");
+  data_out.build_patches ();
+
+  std::ostringstream filename;
+  filename << "solution-"
+           << cycle
+           << ".vtk";
+
+//  std::ofstream output (filename.str().c_str());
+//  data_out.write_vtk (output);
+}
+
+
+// @sect4{LaplaceProblem::run}
+
+// Like several of the functions above, this
+// is almost exactly a copy of of the
+// corresponding function in step-6. The only
+// difference is the call to
+// <code>assemble_multigrid</code> that takes
+// care of forming the matrices on every
+// level that we need in the multigrid
+// method.
+template <int dim>
+void LaplaceProblem<dim>::run ()
+{
+  for (unsigned int cycle=0; cycle<8; ++cycle)
+    {
+      deallog << "Cycle " << cycle << ':' << std::endl;
+
+      if (cycle == 0)
+        {
+          GridGenerator::hyper_ball (triangulation);
+
+          static const HyperBallBoundary<dim> boundary;
+          triangulation.set_boundary (0, boundary);
+
+          triangulation.refine_global (1);
+        }
+      else
+        refine_grid ();
+
+
+      deallog << "   Number of active cells:       "
+              << triangulation.n_active_cells()
+              << std::endl;
+
+      setup_system ();
+
+      deallog << "   Number of degrees of freedom: "
+              << mg_dof_handler.n_dofs()
+              << " (by level: ";
+      for (unsigned int level=0; level<triangulation.n_levels(); ++level)
+        deallog << mg_dof_handler.n_dofs(level)
+                << (level == triangulation.n_levels()-1
+                    ? ")" : ", ");
+      deallog << std::endl;
+
+      assemble_system ();
+      assemble_multigrid ();
+
+      solve ();
+//      output_results (cycle);
+    }
+}
+
+
+// @sect3{The main() function}
+//
+// This is again the same function as
+// in step-6:
+int main ()
+{
+  std::ofstream logfile("step-16/output");
+  deallog << std::setprecision(4);
+  deallog.attach(logfile);
+  deallog.depth_console(0);
+  deallog.threshold_double(1.e-10);
+
+  try
+    {
+      deallog.depth_console (0);
+
+      LaplaceProblem<2> laplace_problem(1);
+      laplace_problem.run ();
+    }
+  catch (std::exception &exc)
+    {
+      std::cerr << std::endl << std::endl
+                << "----------------------------------------------------"
+                << std::endl;
+      std::cerr << "Exception on processing: " << std::endl
+                << exc.what() << std::endl
+                << "Aborting!" << std::endl
+                << "----------------------------------------------------"
+                << std::endl;
+
+      return 1;
+    }
+  catch (...)
+    {
+      std::cerr << std::endl << std::endl
+                << "----------------------------------------------------"
+                << std::endl;
+      std::cerr << "Unknown exception!" << std::endl
+                << "Aborting!" << std::endl
+                << "----------------------------------------------------"
+                << std::endl;
+      return 1;
+    }
+
+  return 0;
+}
diff --git a/tests/multigrid/step-16-02/cmp/generic b/tests/multigrid/step-16-02/cmp/generic
new file mode 100644 (file)
index 0000000..4cbc822
--- /dev/null
@@ -0,0 +1,57 @@
+
+DEAL::Cycle 0:
+DEAL::   Number of active cells:       20
+DEAL::Number of degrees of freedom: 25   L0: 8   L1: 25
+DEAL::   Number of degrees of freedom: 25 (by level: 8, 25)
+DEAL:cg::Starting value 0.5107
+DEAL:cg::Convergence step 7 value 0
+DEAL::   7 CG iterations needed to obtain convergence.
+DEAL::Cycle 1:
+DEAL::   Number of active cells:       44
+DEAL::Number of degrees of freedom: 57   L0: 8   L1: 25   L2: 48
+DEAL::   Number of degrees of freedom: 57 (by level: 8, 25, 48)
+DEAL:cg::Starting value 0.4679
+DEAL:cg::Convergence step 8 value 0
+DEAL::   8 CG iterations needed to obtain convergence.
+DEAL::Cycle 2:
+DEAL::   Number of active cells:       92
+DEAL::Number of degrees of freedom: 117   L0: 8   L1: 25   L2: 80   L3: 60
+DEAL::   Number of degrees of freedom: 117 (by level: 8, 25, 80, 60)
+DEAL:cg::Starting value 0.3390
+DEAL:cg::Convergence step 9 value 0
+DEAL::   9 CG iterations needed to obtain convergence.
+DEAL::Cycle 3:
+DEAL::   Number of active cells:       188
+DEAL::Number of degrees of freedom: 221   L0: 8   L1: 25   L2: 80   L3: 200
+DEAL::   Number of degrees of freedom: 221 (by level: 8, 25, 80, 200)
+DEAL:cg::Starting value 0.2689
+DEAL:cg::Convergence step 12 value 0
+DEAL::   12 CG iterations needed to obtain convergence.
+DEAL::Cycle 4:
+DEAL::   Number of active cells:       416
+DEAL::Number of degrees of freedom: 485   L0: 8   L1: 25   L2: 89   L3: 288   L4: 280
+DEAL::   Number of degrees of freedom: 485 (by level: 8, 25, 89, 288, 280)
+DEAL:cg::Starting value 0.1841
+DEAL:cg::Convergence step 13 value 0
+DEAL::   13 CG iterations needed to obtain convergence.
+DEAL::Cycle 5:
+DEAL::   Number of active cells:       800
+DEAL::Number of degrees of freedom: 925   L0: 8   L1: 25   L2: 89   L3: 288   L4: 784   L5: 132
+DEAL::   Number of degrees of freedom: 925 (by level: 8, 25, 89, 288, 784, 132)
+DEAL:cg::Starting value 0.1440
+DEAL:cg::Convergence step 14 value 0
+DEAL::   14 CG iterations needed to obtain convergence.
+DEAL::Cycle 6:
+DEAL::   Number of active cells:       1628
+DEAL::Number of degrees of freedom: 1865   L0: 8   L1: 25   L2: 89   L3: 304   L4: 1000   L5: 1164   L6: 72
+DEAL::   Number of degrees of freedom: 1865 (by level: 8, 25, 89, 304, 1000, 1164, 72)
+DEAL:cg::Starting value 0.1174
+DEAL:cg::Convergence step 14 value 0
+DEAL::   14 CG iterations needed to obtain convergence.
+DEAL::Cycle 7:
+DEAL::   Number of active cells:       3194
+DEAL::Number of degrees of freedom: 3603   L0: 8   L1: 25   L2: 89   L3: 328   L4: 1032   L5: 2200   L6: 1392
+DEAL::   Number of degrees of freedom: 3603 (by level: 8, 25, 89, 328, 1032, 2200, 1392)
+DEAL:cg::Starting value 0.09098
+DEAL:cg::Convergence step 16 value 0
+DEAL::   16 CG iterations needed to obtain convergence.

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