]> https://gitweb.dealii.org/ - dealii.git/commitdiff
Tests for minlevel>0.
authorMartin Kronbichler <kronbichler@lnm.mw.tum.de>
Sun, 3 Apr 2016 11:11:26 +0000 (13:11 +0200)
committerMartin Kronbichler <kronbichler@lnm.mw.tum.de>
Sun, 3 Apr 2016 11:12:53 +0000 (13:12 +0200)
tests/multigrid/step-16-03.cc [new file with mode: 0644]
tests/multigrid/step-16-03.output [new file with mode: 0644]
tests/multigrid/step-16-04.cc [new file with mode: 0644]
tests/multigrid/step-16-04.output [new file with mode: 0644]

diff --git a/tests/multigrid/step-16-03.cc b/tests/multigrid/step-16-03.cc
new file mode 100644 (file)
index 0000000..4630093
--- /dev/null
@@ -0,0 +1,519 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2003 - 2015 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.
+//
+// ---------------------------------------------------------------------
+
+// Similar to step-16 but starting the mg hierarchy at level 2 rather than
+// level 0
+
+#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/error_estimator.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 ();
+
+  Triangulation<dim>   triangulation;
+  FE_Q<dim>            fe;
+  DoFHandler<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;
+  const unsigned int min_level;
+
+  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),
+  min_level(2)
+{}
+
+
+template <int dim>
+void LaplaceProblem<dim>::setup_system ()
+{
+  mg_dof_handler.distribute_dofs(fe);
+  mg_dof_handler.distribute_mg_dofs (fe);
+
+  sparsity_pattern.reinit (mg_dof_handler.n_dofs(),
+                           mg_dof_handler.n_dofs(),
+                           mg_dof_handler.max_couplings_between_dofs());
+  DoFTools::make_sparsity_pattern (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;
+  MappingQGeneric<dim> mapping(1);
+  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(min_level, n_levels-1);
+  mg_interface_matrices.clear ();
+  mg_matrices.resize(min_level, n_levels-1);
+  mg_matrices.clear ();
+  mg_sparsity_patterns.resize(min_level, n_levels-1);
+
+  for (unsigned int level=min_level; 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 DoFHandler<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<ConstraintMatrix> boundary_constraints (triangulation.n_levels());
+  ConstraintMatrix empty_constraints;
+  for (unsigned int level=min_level; level<triangulation.n_levels(); ++level)
+    {
+      boundary_constraints[level].add_lines (mg_constrained_dofs.get_refinement_edge_indices(level));
+      boundary_constraints[level].add_lines (mg_constrained_dofs.get_boundary_indices(level));
+      boundary_constraints[level].close ();
+    }
+
+  typename DoFHandler<dim>::cell_iterator cell = mg_dof_handler.begin(min_level),
+                                          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()]);
+
+      const unsigned int lvl = cell->level();
+
+      for (unsigned int i=0; i<dofs_per_cell; ++i)
+        for (unsigned int j=0; j<dofs_per_cell; ++j)
+          if (mg_constrained_dofs.at_refinement_edge(lvl, local_dof_indices[i])
+              &&
+              ! mg_constrained_dofs.at_refinement_edge(lvl, local_dof_indices[j])
+              &&
+              (
+                (!mg_constrained_dofs.is_boundary_index(lvl, local_dof_indices[i])
+                 &&
+                 !mg_constrained_dofs.is_boundary_index(lvl, local_dof_indices[j])
+                ) // ( !boundary(i) && !boundary(j) )
+                ||
+                (
+                  mg_constrained_dofs.is_boundary_index(lvl, local_dof_indices[i])
+                  &&
+                  local_dof_indices[i]==local_dof_indices[j]
+                ) // ( boundary(i) && boundary(j) && i==j )
+              )
+             )
+            {
+              // do nothing, so add entries to interface matrix
+            }
+          else
+            {
+              cell_matrix(i,j) = 0;
+            }
+
+
+      empty_constraints
+      .distribute_local_to_global (cell_matrix,
+                                   local_dof_indices,
+                                   mg_interface_matrices[cell->level()]);
+    }
+}
+
+
+
+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[min_level]);
+  deallog << "   Size of coarse grid matrix: " << coarse_matrix.m() << std::endl;
+  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);
+
+  mg::Matrix<> mg_matrix(mg_matrices);
+  mg::Matrix<> mg_interface_up(mg_interface_matrices);
+  mg::Matrix<> mg_interface_down(mg_interface_matrices);
+
+  Multigrid<Vector<double> > mg(min_level,
+                                triangulation.n_global_levels()-1,
+                                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;
+}
+
+
+
+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>::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 (min_level);
+        }
+      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=min_level; 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 ();
+    }
+}
+
+
+// @sect3{The main() function}
+//
+// This is again the same function as
+// in step-6:
+int main ()
+{
+  std::ofstream logfile("output");
+  deallog << std::setprecision(4);
+  deallog.attach(logfile);
+  deallog.threshold_double(1.e-10);
+
+  try
+    {
+
+      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-16-03.output b/tests/multigrid/step-16-03.output
new file mode 100644 (file)
index 0000000..b3279bb
--- /dev/null
@@ -0,0 +1,57 @@
+
+DEAL::Cycle 0:
+DEAL::   Number of active cells:       80
+DEAL::   Number of degrees of freedom: 89 (by level: 89)
+DEAL::  Size of coarse grid matrix: 89
+DEAL:cg::Starting value 0.3204
+DEAL:cg::Convergence step 1 value 0
+DEAL::   1 CG iterations needed to obtain convergence.
+DEAL::Cycle 1:
+DEAL::   Number of active cells:       176
+DEAL::   Number of degrees of freedom: 209 (by level: 89, 176)
+DEAL::  Size of coarse grid matrix: 89
+DEAL:cg::Starting value 0.2524
+DEAL:cg::Convergence step 12 value 0
+DEAL::   12 CG iterations needed to obtain convergence.
+DEAL::Cycle 2:
+DEAL::   Number of active cells:       368
+DEAL::   Number of degrees of freedom: 429 (by level: 89, 288, 208)
+DEAL::  Size of coarse grid matrix: 89
+DEAL:cg::Starting value 0.1866
+DEAL:cg::Convergence step 11 value 0
+DEAL::   11 CG iterations needed to obtain convergence.
+DEAL::Cycle 3:
+DEAL::   Number of active cells:       704
+DEAL::   Number of degrees of freedom: 829 (by level: 89, 288, 656, 132)
+DEAL::  Size of coarse grid matrix: 89
+DEAL:cg::Starting value 0.1580
+DEAL:cg::Convergence step 13 value 0
+DEAL::   13 CG iterations needed to obtain convergence.
+DEAL::Cycle 4:
+DEAL::   Number of active cells:       1436
+DEAL::   Number of degrees of freedom: 1597 (by level: 89, 304, 1000, 744, 72)
+DEAL::  Size of coarse grid matrix: 89
+DEAL:cg::Starting value 0.1204
+DEAL:cg::Convergence step 14 value 0
+DEAL::   14 CG iterations needed to obtain convergence.
+DEAL::Cycle 5:
+DEAL::   Number of active cells:       2828
+DEAL::   Number of degrees of freedom: 3213 (by level: 89, 328, 1032, 1700, 1360)
+DEAL::  Size of coarse grid matrix: 89
+DEAL:cg::Starting value 0.09649
+DEAL:cg::Convergence step 18 value 0
+DEAL::   18 CG iterations needed to obtain convergence.
+DEAL::Cycle 6:
+DEAL::   Number of active cells:       5708
+DEAL::   Number of degrees of freedom: 6437 (by level: 89, 328, 1032, 3516, 1728, 2320)
+DEAL::  Size of coarse grid matrix: 89
+DEAL:cg::Starting value 0.07895
+DEAL:cg::Convergence step 27 value 0
+DEAL::   27 CG iterations needed to obtain convergence.
+DEAL::Cycle 7:
+DEAL::   Number of active cells:       11828
+DEAL::   Number of degrees of freedom: 13277 (by level: 89, 328, 1032, 3632, 5092, 3656, 4824)
+DEAL::  Size of coarse grid matrix: 89
+DEAL:cg::Starting value 0.07383
+DEAL:cg::Convergence step 20 value 0
+DEAL::   20 CG iterations needed to obtain convergence.
diff --git a/tests/multigrid/step-16-04.cc b/tests/multigrid/step-16-04.cc
new file mode 100644 (file)
index 0000000..c6c7d77
--- /dev/null
@@ -0,0 +1,529 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2003 - 2015 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.
+//
+// ---------------------------------------------------------------------
+
+// Similar to step-16-03 (starting the mg hierarchy at level 2 rather than
+// level 0) but for parallel::distributed::Vector that has a different code
+// path
+
+#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/base/mpi.h>
+
+#include <deal.II/lac/constraint_matrix.h>
+#include <deal.II/lac/parallel_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/error_estimator.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 ();
+
+  Triangulation<dim>   triangulation;
+  FE_Q<dim>            fe;
+  DoFHandler<dim>      mg_dof_handler;
+
+  SparsityPattern      sparsity_pattern;
+  SparseMatrix<double> system_matrix;
+
+  ConstraintMatrix     hanging_node_constraints;
+  ConstraintMatrix     constraints;
+
+  parallel::distributed::Vector<double> solution;
+  parallel::distributed::Vector<double> system_rhs;
+
+  const unsigned int degree;
+  const unsigned int min_level;
+
+  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),
+  min_level(2)
+{}
+
+
+
+template <int dim>
+void LaplaceProblem<dim>::setup_system ()
+{
+  mg_dof_handler.distribute_dofs(fe);
+  mg_dof_handler.distribute_mg_dofs (fe);
+
+  sparsity_pattern.reinit (mg_dof_handler.n_dofs(),
+                           mg_dof_handler.n_dofs(),
+                           mg_dof_handler.max_couplings_between_dofs());
+  DoFTools::make_sparsity_pattern (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;
+  MappingQGeneric<dim> mapping(1);
+  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(min_level, n_levels-1);
+  mg_interface_matrices.clear ();
+  mg_matrices.resize(min_level, n_levels-1);
+  mg_matrices.clear ();
+  mg_sparsity_patterns.resize(min_level, n_levels-1);
+
+  for (unsigned int level=min_level; 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 ()
+{
+  Vector<double> tmp(system_rhs.size());
+  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 DoFHandler<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, tmp);
+    }
+  for (unsigned int i=0; i<tmp.size(); ++i)
+    system_rhs(i) = tmp(i);
+}
+
+
+
+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<ConstraintMatrix> boundary_constraints (triangulation.n_levels());
+  ConstraintMatrix empty_constraints;
+  for (unsigned int level=min_level; level<triangulation.n_levels(); ++level)
+    {
+      boundary_constraints[level].add_lines (mg_constrained_dofs.get_refinement_edge_indices(level));
+      boundary_constraints[level].add_lines (mg_constrained_dofs.get_boundary_indices(level));
+      boundary_constraints[level].close ();
+    }
+
+  typename DoFHandler<dim>::cell_iterator cell = mg_dof_handler.begin(min_level),
+                                          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()]);
+
+      const unsigned int lvl = cell->level();
+
+      for (unsigned int i=0; i<dofs_per_cell; ++i)
+        for (unsigned int j=0; j<dofs_per_cell; ++j)
+          if (mg_constrained_dofs.at_refinement_edge(lvl, local_dof_indices[i])
+              &&
+              ! mg_constrained_dofs.at_refinement_edge(lvl, local_dof_indices[j])
+              &&
+              (
+                (!mg_constrained_dofs.is_boundary_index(lvl, local_dof_indices[i])
+                 &&
+                 !mg_constrained_dofs.is_boundary_index(lvl, local_dof_indices[j])
+                ) // ( !boundary(i) && !boundary(j) )
+                ||
+                (
+                  mg_constrained_dofs.is_boundary_index(lvl, local_dof_indices[i])
+                  &&
+                  local_dof_indices[i]==local_dof_indices[j]
+                ) // ( boundary(i) && boundary(j) && i==j )
+              )
+             )
+            {
+              // do nothing, so add entries to interface matrix
+            }
+          else
+            {
+              cell_matrix(i,j) = 0;
+            }
+
+
+      empty_constraints
+      .distribute_local_to_global (cell_matrix,
+                                   local_dof_indices,
+                                   mg_interface_matrices[cell->level()]);
+    }
+}
+
+
+
+template <int dim>
+void LaplaceProblem<dim>::solve ()
+{
+  MGTransferPrebuilt<parallel::distributed::Vector<double> >
+  mg_transfer(hanging_node_constraints, mg_constrained_dofs);
+  mg_transfer.build_matrices(mg_dof_handler);
+
+  SolverControl coarse_solver_control (1000, 1e-10, false, false);
+  SolverCG<parallel::distributed::Vector<double> > coarse_solver(coarse_solver_control);
+  PreconditionIdentity id;
+  MGCoarseGridLACIteration<SolverCG<parallel::distributed::Vector<double> >,parallel::distributed::Vector<double> >
+  coarse_grid_solver(coarse_solver, mg_matrices[min_level], id);
+  deallog << "   Size of coarse grid matrix: " << mg_matrices[min_level].m() << std::endl;
+
+  typedef PreconditionChebyshev<SparseMatrix<double>,parallel::distributed::Vector<double> > Smoother;
+  GrowingVectorMemory<parallel::distributed::Vector<double> >   vector_memory;
+  MGSmootherPrecondition<SparseMatrix<double>, Smoother, parallel::distributed::Vector<double> >
+  mg_smoother;
+  typename Smoother::AdditionalData smoother_data;
+  smoother_data.smoothing_range = 20.;
+  smoother_data.degree = 2;
+  smoother_data.eig_cg_n_iterations = 20;
+  mg_smoother.initialize(mg_matrices, smoother_data);
+
+  mg::Matrix<parallel::distributed::Vector<double> > mg_matrix(mg_matrices);
+  mg::Matrix<parallel::distributed::Vector<double> > mg_interface_up(mg_interface_matrices);
+  mg::Matrix<parallel::distributed::Vector<double> > mg_interface_down(mg_interface_matrices);
+
+  Multigrid<parallel::distributed::Vector<double> > mg(min_level,
+                                                       triangulation.n_global_levels()-1,
+                                                       mg_matrix,
+                                                       coarse_grid_solver,
+                                                       mg_transfer,
+                                                       mg_smoother,
+                                                       mg_smoother);
+  mg.set_edge_matrices(mg_interface_down, mg_interface_up);
+
+  PreconditionMG<dim, parallel::distributed::Vector<double>, MGTransferPrebuilt<parallel::distributed::Vector<double> > >
+  preconditioner(mg_dof_handler, mg, mg_transfer);
+
+  SolverControl solver_control (1000, 1e-12);
+  SolverCG<parallel::distributed::Vector<double> > 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;
+}
+
+
+
+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>::run ()
+{
+  for (unsigned int cycle=0; cycle<6; ++cycle)
+    {
+      deallog << "Cycle " << cycle << ':' << std::endl;
+
+      if (cycle == 0)
+        {
+          GridGenerator::hyper_cube (triangulation);
+          triangulation.refine_global (min_level+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=min_level; 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 ();
+    }
+}
+
+
+// @sect3{The main() function}
+//
+// This is again the same function as
+// in step-6:
+int main (int argc, char **argv)
+{
+  std::ofstream logfile("output");
+  deallog << std::setprecision(4);
+  deallog.attach(logfile);
+  deallog.threshold_double(1.e-10);
+
+  Utilities::MPI::MPI_InitFinalize mpi(argc, argv);
+
+  try
+    {
+
+      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-16-04.output b/tests/multigrid/step-16-04.output
new file mode 100644 (file)
index 0000000..7fb681c
--- /dev/null
@@ -0,0 +1,97 @@
+
+DEAL::Cycle 0:
+DEAL::   Number of active cells:       64
+DEAL::   Number of degrees of freedom: 81 (by level: 25, 81)
+DEAL::   Size of coarse grid matrix: 25
+DEAL:cg::Starting value 0.9798
+DEAL:cg::Convergence step 7 value 0
+DEAL:cg::Starting value 0.9938
+DEAL:cg::Convergence step 18 value 0
+DEAL:cg::Starting value 0.1094
+DEAL:cg::Convergence step 10 value 0
+DEAL::   10 CG iterations needed to obtain convergence.
+DEAL::Cycle 1:
+DEAL::   Number of active cells:       127
+DEAL::   Number of degrees of freedom: 160 (by level: 25, 81, 117)
+DEAL::   Size of coarse grid matrix: 25
+DEAL:cg::Starting value 0.9798
+DEAL:cg::Convergence step 7 value 0
+DEAL:cg::Starting value 0.9938
+DEAL:cg::Convergence step 18 value 0
+DEAL:cg::Starting value 0.9957
+DEAL:cg::Convergence step 15 value 0
+DEAL:cg::Starting value 0.09101
+DEAL:cg::Convergence step 13 value 0
+DEAL::   13 CG iterations needed to obtain convergence.
+DEAL::Cycle 2:
+DEAL::   Number of active cells:       256
+DEAL::   Number of degrees of freedom: 301 (by level: 25, 81, 245, 71)
+DEAL::   Size of coarse grid matrix: 25
+DEAL:cg::Starting value 0.9798
+DEAL:cg::Convergence step 7 value 0
+DEAL:cg::Starting value 0.9938
+DEAL:cg::Convergence step 18 value 0
+DEAL:cg::Starting value 0.9980
+DEAL:cg::Failure step 20 value 7.015e-05
+DEAL:cg::Starting value 0.9929
+DEAL:cg::Convergence step 11 value 0
+DEAL:cg::Starting value 0.06376
+DEAL:cg::Convergence step 12 value 0
+DEAL::   12 CG iterations needed to obtain convergence.
+DEAL::Cycle 3:
+DEAL::   Number of active cells:       493
+DEAL::   Number of degrees of freedom: 600 (by level: 25, 81, 265, 376, 119)
+DEAL::   Size of coarse grid matrix: 25
+DEAL:cg::Starting value 0.9798
+DEAL:cg::Convergence step 7 value 0
+DEAL:cg::Starting value 0.9938
+DEAL:cg::Convergence step 18 value 0
+DEAL:cg::Starting value 0.9981
+DEAL:cg::Failure step 20 value 0.0001644
+DEAL:cg::Starting value 0.9987
+DEAL:cg::Failure step 20 value 5.735e-09
+DEAL:cg::Starting value 0.9958
+DEAL:cg::Convergence step 12 value 0
+DEAL:cg::Starting value 0.05706
+DEAL:cg::Convergence step 15 value 0
+DEAL::   15 CG iterations needed to obtain convergence.
+DEAL::Cycle 4:
+DEAL::   Number of active cells:       979
+DEAL::   Number of degrees of freedom: 1093 (by level: 25, 81, 273, 791, 269, 88)
+DEAL::   Size of coarse grid matrix: 25
+DEAL:cg::Starting value 0.9798
+DEAL:cg::Convergence step 7 value 0
+DEAL:cg::Starting value 0.9938
+DEAL:cg::Convergence step 18 value 0
+DEAL:cg::Starting value 0.9982
+DEAL:cg::Failure step 20 value 0.0002935
+DEAL:cg::Starting value 0.9994
+DEAL:cg::Failure step 20 value 0.02813
+DEAL:cg::Starting value 0.9981
+DEAL:cg::Failure step 20 value 1.498e-09
+DEAL:cg::Starting value 0.9943
+DEAL:cg::Convergence step 7 value 0
+DEAL:cg::Starting value 0.04157
+DEAL:cg::Convergence step 15 value 0
+DEAL::   15 CG iterations needed to obtain convergence.
+DEAL::Cycle 5:
+DEAL::   Number of active cells:       1912
+DEAL::   Number of degrees of freedom: 2184 (by level: 25, 81, 277, 961, 1070, 501, 172)
+DEAL::   Size of coarse grid matrix: 25
+DEAL:cg::Starting value 0.9798
+DEAL:cg::Convergence step 7 value 0
+DEAL:cg::Starting value 0.9938
+DEAL:cg::Convergence step 18 value 0
+DEAL:cg::Starting value 0.9982
+DEAL:cg::Failure step 20 value 0.0004177
+DEAL:cg::Starting value 0.9995
+DEAL:cg::Failure step 20 value 0.05428
+DEAL:cg::Starting value 0.9995
+DEAL:cg::Failure step 20 value 0.0001063
+DEAL:cg::Starting value 0.9990
+DEAL:cg::Failure step 20 value 1.860e-09
+DEAL:cg::Starting value 0.9971
+DEAL:cg::Convergence step 13 value 0
+DEAL:cg::Starting value 0.03510
+DEAL:cg::Convergence step 15 value 0
+DEAL::   15 CG iterations needed to obtain convergence.

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