mg_transfer_block.cc

// ---------------------------------------------------------------------
//
// Copyright (C) 2003 - 2019 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.
//
// ---------------------------------------------------------------------


#include <deal.II/base/logstream.h>

#include <deal.II/dofs/dof_accessor.h>
#include <deal.II/dofs/dof_tools.h>

#include <deal.II/fe/fe.h>

#include <deal.II/grid/tria.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/sparse_matrix.h>
#include <deal.II/lac/vector.h>

#include <deal.II/multigrid/mg_tools.h>
#include <deal.II/multigrid/mg_transfer_block.h>
#include <deal.II/multigrid/mg_transfer_block.templates.h>

#include <algorithm>
#include <iostream>
#include <numeric>
#include <utility>

DEAL_II_NAMESPACE_OPEN

namespace
{
  template <int dim, typename number, int spacedim>
  void
  reinit_vector_by_blocks(
    const ::DoFHandler<dim, spacedim> &          mg_dof,
    MGLevelObject<BlockVector<number>> &               v,
    const std::vector<bool> &                          sel,
    std::vector<std::vector<types::global_dof_index>> &ndofs)
  {
    std::vector<bool> selected = sel;
    // Compute the number of blocks needed
    const unsigned int n_selected =
      std::accumulate(selected.begin(), selected.end(), 0u);

    if (ndofs.size() == 0)
      {
        std::vector<std::vector<types::global_dof_index>> new_dofs(
          mg_dof.get_triangulation().n_levels(),
          std::vector<types::global_dof_index>(selected.size()));
        std::swap(ndofs, new_dofs);
        MGTools::count_dofs_per_block(mg_dof, ndofs);
      }

    for (unsigned int level = v.min_level(); level <= v.max_level(); ++level)
      {
        v[level].reinit(n_selected, 0);
        unsigned int k = 0;
        for (unsigned int i = 0;
             i < selected.size() && (k < v[level].n_blocks());
             ++i)
          {
            if (selected[i])
              {
                v[level].block(k++).reinit(ndofs[level][i]);
              }
            v[level].collect_sizes();
          }
      }
  }


  template <int dim, typename number, int spacedim>
  void
  reinit_vector_by_blocks(
    const ::DoFHandler<dim, spacedim> &          mg_dof,
    MGLevelObject<::Vector<number>> &            v,
    const unsigned int                                 selected_block,
    std::vector<std::vector<types::global_dof_index>> &ndofs)
  {
    const unsigned int n_blocks = mg_dof.get_fe().n_blocks();
    Assert(selected_block < n_blocks,
           ExcIndexRange(selected_block, 0, n_blocks));

    std::vector<bool> selected(n_blocks, false);
    selected[selected_block] = true;

    if (ndofs.size() == 0)
      {
        std::vector<std::vector<types::global_dof_index>> new_dofs(
          mg_dof.get_triangulation().n_levels(),
          std::vector<types::global_dof_index>(selected.size()));
        std::swap(ndofs, new_dofs);
        MGTools::count_dofs_per_block(mg_dof, ndofs);
      }

    for (unsigned int level = v.min_level(); level <= v.max_level(); ++level)
      {
        v[level].reinit(ndofs[level][selected_block]);
      }
  }
} // namespace


template <typename number>
template <int dim, typename number2, int spacedim>
void
MGTransferBlockSelect<number>::copy_to_mg(
  const DoFHandler<dim, spacedim> &mg_dof_handler,
  MGLevelObject<Vector<number>> &  dst,
  const BlockVector<number2> &     src) const
{
  reinit_vector_by_blocks(mg_dof_handler, dst, selected_block, sizes);
  // For MGTransferBlockSelect, the
  // multilevel block is always the
  // first, since only one block is
  // selected.
  for (unsigned int level = mg_dof_handler.get_triangulation().n_levels();
       level != 0;)
    {
      --level;
      for (IT i = copy_indices[selected_block][level].begin();
           i != copy_indices[selected_block][level].end();
           ++i)
        dst[level](i->second) = src.block(selected_block)(i->first);
    }
}



template <typename number>
template <int dim, typename number2, int spacedim>
void
MGTransferBlockSelect<number>::copy_to_mg(
  const DoFHandler<dim, spacedim> &mg_dof_handler,
  MGLevelObject<Vector<number>> &  dst,
  const Vector<number2> &          src) const
{
  reinit_vector_by_blocks(mg_dof_handler, dst, selected_block, sizes);
  // For MGTransferBlockSelect, the
  // multilevel block is always the
  // first, since only one block is selected.
  for (unsigned int level = mg_dof_handler.get_triangulation().n_levels();
       level != 0;)
    {
      --level;
      for (IT i = copy_indices[selected_block][level].begin();
           i != copy_indices[selected_block][level].end();
           ++i)
        dst[level](i->second) = src(i->first);
    }
}



template <typename number>
template <int dim, typename number2, int spacedim>
void
MGTransferBlock<number>::copy_to_mg(
  const DoFHandler<dim, spacedim> &   mg_dof_handler,
  MGLevelObject<BlockVector<number>> &dst,
  const BlockVector<number2> &        src) const
{
  reinit_vector_by_blocks(mg_dof_handler, dst, selected, sizes);
  for (unsigned int level = mg_dof_handler.get_triangulation().n_levels();
       level != 0;)
    {
      --level;
      for (unsigned int block = 0; block < selected.size(); ++block)
        if (selected[block])
          for (IT i = copy_indices[block][level].begin();
               i != copy_indices[block][level].end();
               ++i)
            dst[level].block(mg_block[block])(i->second) =
              src.block(block)(i->first);
    }
}



template <int dim, int spacedim>
void
MGTransferBlockBase::build_matrices(const DoFHandler<dim, spacedim> &,
                                    const DoFHandler<dim, spacedim> &mg_dof)
{
  const FiniteElement<dim> &fe            = mg_dof.get_fe();
  const unsigned int        n_blocks      = fe.n_blocks();
  const unsigned int        dofs_per_cell = fe.dofs_per_cell;
  const unsigned int        n_levels = mg_dof.get_triangulation().n_levels();

  Assert(selected.size() == n_blocks,
         ExcDimensionMismatch(selected.size(), n_blocks));

  // Compute the mapping between real
  // blocks and blocks used for
  // multigrid computations.
  mg_block.resize(n_blocks);
  n_mg_blocks = 0;
  for (unsigned int i = 0; i < n_blocks; ++i)
    if (selected[i])
      mg_block[i] = n_mg_blocks++;
    else
      mg_block[i] = numbers::invalid_unsigned_int;

  // Compute the lengths of all blocks
  sizes.clear();
  sizes.resize(n_levels, std::vector<types::global_dof_index>(fe.n_blocks()));
  MGTools::count_dofs_per_block(mg_dof, sizes);

  // Fill some index vectors
  // for later use.
  mg_block_start = sizes;
  // Compute start indices from sizes
  for (auto &level_blocks : mg_block_start)
    {
      types::global_dof_index k = 0;
      for (types::global_dof_index &level_block_start : level_blocks)
        {
          const types::global_dof_index t = level_block_start;
          level_block_start               = k;
          k += t;
        }
    }

  block_start.resize(n_blocks);
  DoFTools::count_dofs_per_block(
    static_cast<const DoFHandler<dim, spacedim> &>(mg_dof), block_start);

  types::global_dof_index k = 0;
  for (types::global_dof_index &first_index : block_start)
    {
      const types::global_dof_index t = first_index;
      first_index                     = k;
      k += t;
    }
  // Build index vectors for
  // copy_to_mg and
  // copy_from_mg. These vectors must
  // be prebuilt, since the
  // get_dof_indices functions are
  // too slow
  copy_indices.resize(n_blocks);
  for (unsigned int block = 0; block < n_blocks; ++block)
    if (selected[block])
      copy_indices[block].resize(n_levels);

  // Building the prolongation matrices starts here!

  // reset the size of the array of
  // matrices. call resize(0) first,
  // in order to delete all elements
  // and clear their memory. then
  // repopulate these arrays
  //
  // note that on resize(0), the
  // shared_ptr class takes care of
  // deleting the object it points to
  // by itself
  prolongation_matrices.resize(0);
  prolongation_sparsities.resize(0);
  prolongation_matrices.reserve(n_levels - 1);
  prolongation_sparsities.reserve(n_levels - 1);

  for (unsigned int i = 0; i < n_levels - 1; ++i)
    {
      prolongation_sparsities.emplace_back(new BlockSparsityPattern);
      prolongation_matrices.emplace_back(new BlockSparseMatrix<double>);
    }

  // two fields which will store the
  // indices of the multigrid dofs
  // for a cell and one of its children
  std::vector<types::global_dof_index> dof_indices_parent(dofs_per_cell);
  std::vector<types::global_dof_index> dof_indices_child(dofs_per_cell);

  // for each level: first build the
  // sparsity pattern of the matrices
  // and then build the matrices
  // themselves. note that we only
  // need to take care of cells on
  // the coarser level which have
  // children

  for (unsigned int level = 0; level < n_levels - 1; ++level)
    {
      // reset the dimension of the
      // structure.  note that for
      // the number of entries per
      // row, the number of parent
      // dofs coupling to a child dof
      // is necessary. this, is the
      // number of degrees of freedom
      // per cell
      prolongation_sparsities[level]->reinit(n_blocks, n_blocks);
      for (unsigned int i = 0; i < n_blocks; ++i)
        for (unsigned int j = 0; j < n_blocks; ++j)
          if (i == j)
            prolongation_sparsities[level]->block(i, j).reinit(
              sizes[level + 1][i], sizes[level][j], dofs_per_cell + 1);
          else
            prolongation_sparsities[level]->block(i, j).reinit(
              sizes[level + 1][i], sizes[level][j], 0);

      prolongation_sparsities[level]->collect_sizes();

      for (typename DoFHandler<dim, spacedim>::cell_iterator cell =
             mg_dof.begin(level);
           cell != mg_dof.end(level);
           ++cell)
        if (cell->has_children())
          {
            cell->get_mg_dof_indices(dof_indices_parent);

            Assert(cell->n_children() ==
                     GeometryInfo<dim>::max_children_per_cell,
                   ExcNotImplemented());
            for (unsigned int child = 0; child < cell->n_children(); ++child)
              {
                // set an alias to the
                // prolongation matrix for
                // this child
                const FullMatrix<double> &prolongation =
                  mg_dof.get_fe().get_prolongation_matrix(
                    child, cell->refinement_case());

                cell->child(child)->get_mg_dof_indices(dof_indices_child);

                // now tag the entries in the
                // matrix which will be used
                // for this pair of parent/child
                for (unsigned int i = 0; i < dofs_per_cell; ++i)
                  for (unsigned int j = 0; j < dofs_per_cell; ++j)
                    if (prolongation(i, j) != 0)
                      {
                        const unsigned int icomp =
                          fe.system_to_block_index(i).first;
                        const unsigned int jcomp =
                          fe.system_to_block_index(j).first;
                        if ((icomp == jcomp) && selected[icomp])
                          prolongation_sparsities[level]->add(
                            dof_indices_child[i], dof_indices_parent[j]);
                      }
              }
          }
      prolongation_sparsities[level]->compress();

      prolongation_matrices[level]->reinit(*prolongation_sparsities[level]);
      // now actually build the matrices
      for (typename DoFHandler<dim, spacedim>::cell_iterator cell =
             mg_dof.begin(level);
           cell != mg_dof.end(level);
           ++cell)
        if (cell->has_children())
          {
            cell->get_mg_dof_indices(dof_indices_parent);

            Assert(cell->n_children() ==
                     GeometryInfo<dim>::max_children_per_cell,
                   ExcNotImplemented());
            for (unsigned int child = 0; child < cell->n_children(); ++child)
              {
                // set an alias to the
                // prolongation matrix for
                // this child
                const FullMatrix<double> &prolongation =
                  mg_dof.get_fe().get_prolongation_matrix(
                    child, cell->refinement_case());

                cell->child(child)->get_mg_dof_indices(dof_indices_child);

                // now set the entries in the
                // matrix
                for (unsigned int i = 0; i < dofs_per_cell; ++i)
                  for (unsigned int j = 0; j < dofs_per_cell; ++j)
                    if (prolongation(i, j) != 0)
                      {
                        const unsigned int icomp =
                          fe.system_to_block_index(i).first;
                        const unsigned int jcomp =
                          fe.system_to_block_index(j).first;
                        if ((icomp == jcomp) && selected[icomp])
                          prolongation_matrices[level]->set(
                            dof_indices_child[i],
                            dof_indices_parent[j],
                            prolongation(i, j));
                      }
              }
          }
    }
  // impose boundary conditions
  // but only in the column of
  // the prolongation matrix
  if (mg_constrained_dofs != nullptr &&
      mg_constrained_dofs->have_boundary_indices())
    {
      std::vector<types::global_dof_index> constrain_indices;
      std::vector<std::vector<bool>>       constraints_per_block(n_blocks);
      for (int level = n_levels - 2; level >= 0; --level)
        {
          if (mg_constrained_dofs->get_boundary_indices(level).n_elements() ==
              0)
            continue;

          // need to delete all the columns in the
          // matrix that are on the boundary. to achieve
          // this, create an array as long as there are
          // matrix columns, and find which columns we
          // need to filter away.
          constrain_indices.resize(0);
          constrain_indices.resize(prolongation_matrices[level]->n(), 0);
          IndexSet::ElementIterator
            dof  = mg_constrained_dofs->get_boundary_indices(level).begin(),
            endd = mg_constrained_dofs->get_boundary_indices(level).end();
          for (; dof != endd; ++dof)
            constrain_indices[*dof] = 1;

          unsigned int index = 0;
          for (unsigned int block = 0; block < n_blocks; ++block)
            {
              const types::global_dof_index n_dofs =
                prolongation_matrices[level]->block(block, block).m();
              constraints_per_block[block].resize(0);
              constraints_per_block[block].resize(n_dofs, false);
              for (types::global_dof_index i = 0; i < n_dofs; ++i, ++index)
                constraints_per_block[block][i] =
                  (constrain_indices[index] == 1);

              for (types::global_dof_index i = 0; i < n_dofs; ++i)
                {
                  SparseMatrix<double>::iterator
                    start_row = prolongation_matrices[level]
                                  ->block(block, block)
                                  .begin(i),
                    end_row =
                      prolongation_matrices[level]->block(block, block).end(i);
                  for (; start_row != end_row; ++start_row)
                    {
                      if (constraints_per_block[block][start_row->column()])
                        start_row->value() = 0.;
                    }
                }
            }
        }
    }
}



template <typename number>
template <int dim, int spacedim>
void
MGTransferBlockSelect<number>::build_matrices(
  const DoFHandler<dim, spacedim> &dof,
  const DoFHandler<dim, spacedim> &mg_dof,
  unsigned int                     select)
{
  const FiniteElement<dim> &fe       = mg_dof.get_fe();
  unsigned int              n_blocks = mg_dof.get_fe().n_blocks();

  selected_block = select;
  selected.resize(n_blocks, false);
  selected[select] = true;

  MGTransferBlockBase::build_matrices(dof, mg_dof);

  std::vector<types::global_dof_index> temp_copy_indices;
  std::vector<types::global_dof_index> global_dof_indices(fe.dofs_per_cell);
  std::vector<types::global_dof_index> level_dof_indices(fe.dofs_per_cell);

  for (int level = dof.get_triangulation().n_levels() - 1; level >= 0; --level)
    {
      typename DoFHandler<dim, spacedim>::active_cell_iterator level_cell =
        mg_dof.begin_active(level);
      const typename DoFHandler<dim, spacedim>::active_cell_iterator level_end =
        mg_dof.end_active(level);

      temp_copy_indices.resize(0);
      temp_copy_indices.resize(sizes[level][selected_block],
                               numbers::invalid_dof_index);

      // Compute coarse level right hand side
      // by restricting from fine level.
      for (; level_cell != level_end; ++level_cell)
        {
          // get the dof numbers of
          // this cell for the global
          // and the level-wise
          // numbering
          level_cell->get_dof_indices(global_dof_indices);
          level_cell->get_mg_dof_indices(level_dof_indices);

          for (unsigned int i = 0; i < fe.dofs_per_cell; ++i)
            {
              const unsigned int block = fe.system_to_block_index(i).first;
              if (selected[block])
                {
                  if (mg_constrained_dofs != nullptr)
                    {
                      if (!mg_constrained_dofs->at_refinement_edge(
                            level, level_dof_indices[i]))
                        temp_copy_indices[level_dof_indices[i] -
                                          mg_block_start[level][block]] =
                          global_dof_indices[i] - block_start[block];
                    }
                  else
                    temp_copy_indices[level_dof_indices[i] -
                                      mg_block_start[level][block]] =
                      global_dof_indices[i] - block_start[block];
                }
            }
        }

      // now all the active dofs got a valid entry,
      // the other ones have an invalid entry. Count
      // the invalid entries and then resize the
      // copy_indices object. Then, insert the pairs
      // of global index and level index into
      // copy_indices.
      const types::global_dof_index n_active_dofs =
        std::count_if(temp_copy_indices.begin(),
                      temp_copy_indices.end(),
                      std::bind(std::not_equal_to<types::global_dof_index>(),
                                std::placeholders::_1,
                                numbers::invalid_dof_index));
      copy_indices[selected_block][level].resize(n_active_dofs);
      types::global_dof_index counter = 0;
      for (types::global_dof_index i = 0; i < temp_copy_indices.size(); ++i)
        if (temp_copy_indices[i] != numbers::invalid_dof_index)
          copy_indices[selected_block][level][counter++] =
            std::pair<types::global_dof_index, unsigned int>(
              temp_copy_indices[i], i);
      Assert(counter == n_active_dofs, ExcInternalError());
    }
}



template <typename number>
template <int dim, int spacedim>
void
MGTransferBlock<number>::build_matrices(const DoFHandler<dim, spacedim> &dof,
                                        const DoFHandler<dim, spacedim> &mg_dof,
                                        const std::vector<bool> &        sel)
{
  const FiniteElement<dim> &fe       = mg_dof.get_fe();
  unsigned int              n_blocks = mg_dof.get_fe().n_blocks();

  if (sel.size() != 0)
    {
      Assert(sel.size() == n_blocks,
             ExcDimensionMismatch(sel.size(), n_blocks));
      selected = sel;
    }
  if (selected.size() == 0)
    selected = std::vector<bool>(n_blocks, true);

  MGTransferBlockBase::build_matrices(dof, mg_dof);

  std::vector<std::vector<types::global_dof_index>> temp_copy_indices(n_blocks);
  std::vector<types::global_dof_index> global_dof_indices(fe.dofs_per_cell);
  std::vector<types::global_dof_index> level_dof_indices(fe.dofs_per_cell);
  for (int level = dof.get_triangulation().n_levels() - 1; level >= 0; --level)
    {
      typename DoFHandler<dim, spacedim>::active_cell_iterator level_cell =
        mg_dof.begin_active(level);
      const typename DoFHandler<dim, spacedim>::active_cell_iterator level_end =
        mg_dof.end_active(level);

      for (unsigned int block = 0; block < n_blocks; ++block)
        if (selected[block])
          {
            temp_copy_indices[block].resize(0);
            temp_copy_indices[block].resize(sizes[level][block],
                                            numbers::invalid_dof_index);
          }

      // Compute coarse level right hand side
      // by restricting from fine level.
      for (; level_cell != level_end; ++level_cell)
        {
          // get the dof numbers of
          // this cell for the global
          // and the level-wise
          // numbering
          level_cell->get_dof_indices(global_dof_indices);
          level_cell->get_mg_dof_indices(level_dof_indices);

          for (unsigned int i = 0; i < fe.dofs_per_cell; ++i)
            {
              const unsigned int block = fe.system_to_block_index(i).first;
              if (selected[block])
                temp_copy_indices[block][level_dof_indices[i] -
                                         mg_block_start[level][block]] =
                  global_dof_indices[i] - block_start[block];
            }
        }

      for (unsigned int block = 0; block < n_blocks; ++block)
        if (selected[block])
          {
            const types::global_dof_index n_active_dofs = std::count_if(
              temp_copy_indices[block].begin(),
              temp_copy_indices[block].end(),
              std::bind(std::not_equal_to<types::global_dof_index>(),
                        std::placeholders::_1,
                        numbers::invalid_dof_index));
            copy_indices[block][level].resize(n_active_dofs);
            types::global_dof_index counter = 0;
            for (types::global_dof_index i = 0;
                 i < temp_copy_indices[block].size();
                 ++i)
              if (temp_copy_indices[block][i] != numbers::invalid_dof_index)
                copy_indices[block][level][counter++] =
                  std::pair<types::global_dof_index, unsigned int>(
                    temp_copy_indices[block][i], i);
            Assert(counter == n_active_dofs, ExcInternalError());
          }
    }
}



// explicit instantiations
#include "mg_transfer_block.inst"


DEAL_II_NAMESPACE_CLOSE