mg_transfer_internal.cc

// ---------------------------------------------------------------------
//
// Copyright (C) 2016 - 2018 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/distributed/tria.h>

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

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

#include <deal.II/matrix_free/shape_info.h>

#include <deal.II/multigrid/mg_transfer_internal.h>

DEAL_II_NAMESPACE_OPEN

namespace internal
{
  namespace MGTransfer
  {
    // Internal data structure that is used in the MPI communication in
    // fill_copy_indices().  It represents an entry in the copy_indices* map,
    // that associates a level dof index with a global dof index.
    struct DoFPair
    {
      unsigned int            level;
      types::global_dof_index global_dof_index;
      types::global_dof_index level_dof_index;

      DoFPair(const unsigned int            level,
              const types::global_dof_index global_dof_index,
              const types::global_dof_index level_dof_index)
        : level(level)
        , global_dof_index(global_dof_index)
        , level_dof_index(level_dof_index)
      {}

      DoFPair()
        : level(numbers::invalid_unsigned_int)
        , global_dof_index(numbers::invalid_dof_index)
        , level_dof_index(numbers::invalid_dof_index)
      {}
    };



    template <int dim, int spacedim>
    void
    fill_copy_indices(
      const ::DoFHandler<dim, spacedim> &mg_dof,
      const MGConstrainedDoFs *                mg_constrained_dofs,
      std::vector<std::vector<
        std::pair<types::global_dof_index, types::global_dof_index>>>
        &copy_indices,
      std::vector<std::vector<
        std::pair<types::global_dof_index, types::global_dof_index>>>
        &copy_indices_global_mine,
      std::vector<std::vector<
        std::pair<types::global_dof_index, types::global_dof_index>>>
        &        copy_indices_level_mine,
      const bool skip_interface_dofs)
    {
      // Now we are filling the variables copy_indices*, which are essentially
      // maps from global to mgdof for each level stored as a std::vector of
      // pairs. We need to split this map on each level depending on the
      // ownership of the global and mgdof, so that we later do not access
      // non-local elements in copy_to/from_mg.
      // We keep track in the bitfield dof_touched which global dof has been
      // processed already (on the current level). This is the same as the
      // multigrid running in serial.

      // map cpu_index -> vector of data
      // that will be copied into copy_indices_level_mine
      std::vector<DoFPair> send_data_temp;

      const unsigned int n_levels =
        mg_dof.get_triangulation().n_global_levels();
      copy_indices.resize(n_levels);
      copy_indices_global_mine.resize(n_levels);
      copy_indices_level_mine.resize(n_levels);
      IndexSet globally_relevant;
      DoFTools::extract_locally_relevant_dofs(mg_dof, globally_relevant);

      const unsigned int dofs_per_cell = mg_dof.get_fe().dofs_per_cell;
      std::vector<types::global_dof_index> global_dof_indices(dofs_per_cell);
      std::vector<types::global_dof_index> level_dof_indices(dofs_per_cell);

      for (unsigned int level = 0; level < n_levels; ++level)
        {
          std::vector<bool> dof_touched(globally_relevant.n_elements(), false);
          copy_indices[level].clear();
          copy_indices_level_mine[level].clear();
          copy_indices_global_mine[level].clear();

          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 (; level_cell != level_end; ++level_cell)
            {
              if (mg_dof.get_triangulation().locally_owned_subdomain() !=
                    numbers::invalid_subdomain_id &&
                  (level_cell->level_subdomain_id() ==
                     numbers::artificial_subdomain_id ||
                   level_cell->subdomain_id() ==
                     numbers::artificial_subdomain_id))
                continue;

              // 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 < dofs_per_cell; ++i)
                {
                  // we need to ignore if the DoF is on a refinement edge
                  // (hanging node)
                  if (skip_interface_dofs && mg_constrained_dofs != nullptr &&
                      mg_constrained_dofs->at_refinement_edge(
                        level, level_dof_indices[i]))
                    continue;

                  types::global_dof_index global_idx =
                    globally_relevant.index_within_set(global_dof_indices[i]);
                  // skip if we did this global dof already (on this or a
                  // coarser level)
                  if (dof_touched[global_idx])
                    continue;
                  bool global_mine = mg_dof.locally_owned_dofs().is_element(
                    global_dof_indices[i]);
                  bool level_mine =
                    mg_dof.locally_owned_mg_dofs(level).is_element(
                      level_dof_indices[i]);


                  if (global_mine && level_mine)
                    {
                      copy_indices[level].emplace_back(global_dof_indices[i],
                                                       level_dof_indices[i]);
                    }
                  else if (global_mine)
                    {
                      copy_indices_global_mine[level].emplace_back(
                        global_dof_indices[i], level_dof_indices[i]);

                      // send this to the owner of the level_dof:
                      send_data_temp.emplace_back(level,
                                                  global_dof_indices[i],
                                                  level_dof_indices[i]);
                    }
                  else
                    {
                      // somebody will send those to me
                    }

                  dof_touched[global_idx] = true;
                }
            }
        }

      const ::parallel::Triangulation<dim, spacedim> *tria =
        (dynamic_cast<const parallel::Triangulation<dim, spacedim> *>(
          &mg_dof.get_triangulation()));
      AssertThrow(
        send_data_temp.size() == 0 || tria != nullptr,
        ExcMessage(
          "We should only be sending information with a parallel Triangulation!"));

#ifdef DEAL_II_WITH_MPI
      if (tria)
        {
          // TODO: Searching the owner for every single DoF becomes quite
          // inefficient. Please fix this, Timo.
          // The list of neighbors is symmetric (our neighbors have us as a
          // neighbor), so we can use it to send and to know how many messages
          // we will get.
          const std::set<types::subdomain_id> &neighbors =
            tria->level_ghost_owners();
          std::map<int, std::vector<DoFPair>> send_data;

          // * find owners of the level dofs and insert into send_data
          // accordingly
          for (typename std::vector<DoFPair>::iterator dofpair =
                 send_data_temp.begin();
               dofpair != send_data_temp.end();
               ++dofpair)
            {
              std::set<types::subdomain_id>::iterator it;
              for (it = neighbors.begin(); it != neighbors.end(); ++it)
                {
                  if (mg_dof
                        .locally_owned_mg_dofs_per_processor(
                          dofpair->level)[*it]
                        .is_element(dofpair->level_dof_index))
                    {
                      send_data[*it].push_back(*dofpair);
                      break;
                    }
                }
              // Is this level dof not owned by any of our neighbors? That would
              // certainly be a bug!
              Assert(it != neighbors.end(),
                     ExcMessage("could not find DoF owner."));
            }

          // * send
          std::vector<MPI_Request> requests;
          {
            for (std::set<types::subdomain_id>::iterator it = neighbors.begin();
                 it != neighbors.end();
                 ++it)
              {
                requests.push_back(MPI_Request());
                unsigned int          dest = *it;
                std::vector<DoFPair> &data = send_data[dest];
                // If there is nothing to send, we still need to send a message,
                // because the receiving end will be waitng. In that case we
                // just send an empty message.
                if (data.size())
                  {
                    const int ierr = MPI_Isend(data.data(),
                                               data.size() * sizeof(data[0]),
                                               MPI_BYTE,
                                               dest,
                                               71,
                                               tria->get_communicator(),
                                               &*requests.rbegin());
                    AssertThrowMPI(ierr);
                  }
                else
                  {
                    const int ierr = MPI_Isend(nullptr,
                                               0,
                                               MPI_BYTE,
                                               dest,
                                               71,
                                               tria->get_communicator(),
                                               &*requests.rbegin());
                    AssertThrowMPI(ierr);
                  }
              }
          }

          // * receive
          {
            // We should get one message from each of our neighbors
            std::vector<DoFPair> receive_buffer;
            for (unsigned int counter = 0; counter < neighbors.size();
                 ++counter)
              {
                MPI_Status status;
                int        len;
                int        ierr = MPI_Probe(MPI_ANY_SOURCE,
                                     71,
                                     tria->get_communicator(),
                                     &status);
                AssertThrowMPI(ierr);
                ierr = MPI_Get_count(&status, MPI_BYTE, &len);
                AssertThrowMPI(ierr);

                if (len == 0)
                  {
                    ierr = MPI_Recv(nullptr,
                                    0,
                                    MPI_BYTE,
                                    status.MPI_SOURCE,
                                    status.MPI_TAG,
                                    tria->get_communicator(),
                                    &status);
                    AssertThrowMPI(ierr);
                    continue;
                  }

                int count = len / sizeof(DoFPair);
                Assert(static_cast<int>(count * sizeof(DoFPair)) == len,
                       ExcInternalError());
                receive_buffer.resize(count);

                void *ptr = receive_buffer.data();
                ierr      = MPI_Recv(ptr,
                                len,
                                MPI_BYTE,
                                status.MPI_SOURCE,
                                status.MPI_TAG,
                                tria->get_communicator(),
                                &status);
                AssertThrowMPI(ierr);

                for (unsigned int i = 0; i < receive_buffer.size(); ++i)
                  {
                    copy_indices_level_mine[receive_buffer[i].level]
                      .emplace_back(receive_buffer[i].global_dof_index,
                                    receive_buffer[i].level_dof_index);
                  }
              }
          }

          // * wait for all MPI_Isend to complete
          if (requests.size() > 0)
            {
              const int ierr = MPI_Waitall(requests.size(),
                                           requests.data(),
                                           MPI_STATUSES_IGNORE);
              AssertThrowMPI(ierr);
              requests.clear();
            }
#  ifdef DEBUG
          // Make sure in debug mode, that everybody sent/received all packages
          // on this level. If a deadlock occurs here, the list of expected
          // senders is not computed correctly.
          const int ierr = MPI_Barrier(tria->get_communicator());
          AssertThrowMPI(ierr);
#  endif
        }
#endif

      // Sort the indices. This will produce more reliable debug output for
      // regression tests and likely won't hurt performance even in release
      // mode.
      std::less<std::pair<types::global_dof_index, types::global_dof_index>>
        compare;
      for (unsigned int level = 0; level < copy_indices.size(); ++level)
        std::sort(copy_indices[level].begin(),
                  copy_indices[level].end(),
                  compare);
      for (unsigned int level = 0; level < copy_indices_level_mine.size();
           ++level)
        std::sort(copy_indices_level_mine[level].begin(),
                  copy_indices_level_mine[level].end(),
                  compare);
      for (unsigned int level = 0; level < copy_indices_global_mine.size();
           ++level)
        std::sort(copy_indices_global_mine[level].begin(),
                  copy_indices_global_mine[level].end(),
                  compare);
    }



    // initialize the vectors needed for the transfer (and merge with the
    // content in copy_indices_global_mine)
    template <typename Number>
    void
    reinit_ghosted_vector(
      const IndexSet &                            locally_owned,
      std::vector<types::global_dof_index> &      ghosted_level_dofs,
      const MPI_Comm &                            communicator,
      LinearAlgebra::distributed::Vector<Number> &ghosted_level_vector,
      std::vector<std::pair<unsigned int, unsigned int>>
        &copy_indices_global_mine)
    {
      std::sort(ghosted_level_dofs.begin(), ghosted_level_dofs.end());
      IndexSet ghosted_dofs(locally_owned.size());
      ghosted_dofs.add_indices(ghosted_level_dofs.begin(),
                               std::unique(ghosted_level_dofs.begin(),
                                           ghosted_level_dofs.end()));
      ghosted_dofs.compress();

      // Add possible ghosts from the previous content in the vector
      if (ghosted_level_vector.size() == locally_owned.size())
        {
          // shift the local number of the copy indices according to the new
          // partitioner that we are going to use for the vector
          const auto &part = ghosted_level_vector.get_partitioner();
          ghosted_dofs.add_indices(part->ghost_indices());
          for (unsigned int i = 0; i < copy_indices_global_mine.size(); ++i)
            copy_indices_global_mine[i].second =
              locally_owned.n_elements() +
              ghosted_dofs.index_within_set(
                part->local_to_global(copy_indices_global_mine[i].second));
        }
      ghosted_level_vector.reinit(locally_owned, ghosted_dofs, communicator);
    }

    // Transform the ghost indices to local index space for the vector
    inline void
    copy_indices_to_mpi_local_numbers(
      const Utilities::MPI::Partitioner &         part,
      const std::vector<types::global_dof_index> &mine,
      const std::vector<types::global_dof_index> &remote,
      std::vector<unsigned int> &                 localized_indices)
    {
      localized_indices.resize(mine.size() + remote.size(),
                               numbers::invalid_unsigned_int);
      for (unsigned int i = 0; i < mine.size(); ++i)
        if (mine[i] != numbers::invalid_dof_index)
          localized_indices[i] = part.global_to_local(mine[i]);

      for (unsigned int i = 0; i < remote.size(); ++i)
        if (remote[i] != numbers::invalid_dof_index)
          localized_indices[i + mine.size()] = part.global_to_local(remote[i]);
    }

    // given the collection of child cells in lexicographic ordering as seen
    // from the parent, compute the first index of the given child
    template <int dim>
    unsigned int
    compute_shift_within_children(const unsigned int child,
                                  const unsigned int fe_shift_1d,
                                  const unsigned int fe_degree)
    {
      // we put the degrees of freedom of all child cells in lexicographic
      // ordering
      unsigned int c_tensor_index[dim];
      unsigned int tmp = child;
      for (unsigned int d = 0; d < dim; ++d)
        {
          c_tensor_index[d] = tmp % 2;
          tmp /= 2;
        }
      const unsigned int n_child_dofs_1d = fe_degree + 1 + fe_shift_1d;
      unsigned int       factor          = 1;
      unsigned int       shift           = fe_shift_1d * c_tensor_index[0];
      for (unsigned int d = 1; d < dim; ++d)
        {
          factor *= n_child_dofs_1d;
          shift = shift + factor * fe_shift_1d * c_tensor_index[d];
        }
      return shift;
    }

    // puts the indices on the given child cell in lexicographic ordering with
    // respect to the collection of all child cells as seen from the parent
    template <int dim>
    void
    add_child_indices(
      const unsigned int                          child,
      const unsigned int                          fe_shift_1d,
      const unsigned int                          fe_degree,
      const std::vector<unsigned int> &           lexicographic_numbering,
      const std::vector<types::global_dof_index> &local_dof_indices,
      types::global_dof_index *                   target_indices)
    {
      const unsigned int n_child_dofs_1d = fe_degree + 1 + fe_shift_1d;
      const unsigned int shift =
        compute_shift_within_children<dim>(child, fe_shift_1d, fe_degree);
      const unsigned int n_components =
        local_dof_indices.size() / Utilities::fixed_power<dim>(fe_degree + 1);
      types::global_dof_index *indices = target_indices + shift;
      const unsigned int       n_scalar_cell_dofs =
        Utilities::fixed_power<dim>(n_child_dofs_1d);
      for (unsigned int c = 0, m = 0; c < n_components; ++c)
        for (unsigned int k = 0; k < (dim > 2 ? (fe_degree + 1) : 1); ++k)
          for (unsigned int j = 0; j < (dim > 1 ? (fe_degree + 1) : 1); ++j)
            for (unsigned int i = 0; i < (fe_degree + 1); ++i, ++m)
              {
                const unsigned int index =
                  c * n_scalar_cell_dofs +
                  k * n_child_dofs_1d * n_child_dofs_1d + j * n_child_dofs_1d +
                  i;
                Assert(indices[index] == numbers::invalid_dof_index ||
                         indices[index] ==
                           local_dof_indices[lexicographic_numbering[m]],
                       ExcInternalError());
                indices[index] = local_dof_indices[lexicographic_numbering[m]];
              }
    }

    template <int dim, typename Number>
    void
    setup_element_info(ElementInfo<Number> &          elem_info,
                       const FiniteElement<1> &       fe,
                       const ::DoFHandler<dim> &mg_dof)
    {
      // currently, we have only FE_Q and FE_DGQ type elements implemented
      elem_info.n_components = mg_dof.get_fe().element_multiplicity(0);
      AssertDimension(Utilities::fixed_power<dim>(fe.dofs_per_cell) *
                        elem_info.n_components,
                      mg_dof.get_fe().dofs_per_cell);
      AssertDimension(fe.degree, mg_dof.get_fe().degree);
      elem_info.fe_degree             = fe.degree;
      elem_info.element_is_continuous = fe.dofs_per_vertex > 0;
      Assert(fe.dofs_per_vertex < 2, ExcNotImplemented());

      // step 1.2: get renumbering of 1D basis functions to lexicographic
      // numbers. The distinction according to fe.dofs_per_vertex is to support
      // both continuous and discontinuous bases.
      std::vector<unsigned int> renumbering(fe.dofs_per_cell);
      {
        AssertIndexRange(fe.dofs_per_vertex, 2);
        renumbering[0] = 0;
        for (unsigned int i = 0; i < fe.dofs_per_line; ++i)
          renumbering[i + fe.dofs_per_vertex] =
            GeometryInfo<1>::vertices_per_cell * fe.dofs_per_vertex + i;
        if (fe.dofs_per_vertex > 0)
          renumbering[fe.dofs_per_cell - fe.dofs_per_vertex] =
            fe.dofs_per_vertex;
      }

      // step 1.3: create a dummy 1D quadrature formula to extract the
      // lexicographic numbering for the elements
      std::vector<Point<1>> basic_support_points = fe.get_unit_support_points();
      Assert(fe.dofs_per_vertex == 0 || fe.dofs_per_vertex == 1,
             ExcNotImplemented());
      const unsigned int shift = fe.dofs_per_cell - fe.dofs_per_vertex;
      const unsigned int n_child_dofs_1d =
        (fe.dofs_per_vertex > 0 ? (2 * fe.dofs_per_cell - 1) :
                                  (2 * fe.dofs_per_cell));

      elem_info.n_child_cell_dofs =
        elem_info.n_components * Utilities::fixed_power<dim>(n_child_dofs_1d);
      const Quadrature<1> dummy_quadrature(
        std::vector<Point<1>>(1, Point<1>()));
      internal::MatrixFreeFunctions::ShapeInfo<Number> shape_info;
      shape_info.reinit(dummy_quadrature, mg_dof.get_fe(), 0);
      elem_info.lexicographic_numbering = shape_info.lexicographic_numbering;

      // step 1.4: get the 1d prolongation matrix and combine from both children
      elem_info.prolongation_matrix_1d.resize(fe.dofs_per_cell *
                                              n_child_dofs_1d);

      for (unsigned int c = 0; c < GeometryInfo<1>::max_children_per_cell; ++c)
        for (unsigned int i = 0; i < fe.dofs_per_cell; ++i)
          for (unsigned int j = 0; j < fe.dofs_per_cell; ++j)
            elem_info
              .prolongation_matrix_1d[i * n_child_dofs_1d + j + c * shift] =
              fe.get_prolongation_matrix(c)(renumbering[j], renumbering[i]);
    }

    namespace
    {
      void
      replace(const MGConstrainedDoFs *             mg_constrained_dofs,
              const unsigned int                    level,
              std::vector<types::global_dof_index> &dof_indices)
      {
        if (mg_constrained_dofs != nullptr &&
            mg_constrained_dofs->get_level_constraint_matrix(level)
                .n_constraints() > 0)
          for (auto &ind : dof_indices)
            if (mg_constrained_dofs->get_level_constraint_matrix(level)
                  .is_identity_constrained(ind))
              {
                Assert(mg_constrained_dofs->get_level_constraint_matrix(level)
                           .get_constraint_entries(ind)
                           ->size() == 1,
                       ExcInternalError());
                ind = mg_constrained_dofs->get_level_constraint_matrix(level)
                        .get_constraint_entries(ind)
                        ->front()
                        .first;
              }
      }
    } // namespace

    // Sets up most of the internal data structures of the MGTransferMatrixFree
    // class
    template <int dim, typename Number>
    void
    setup_transfer(
      const ::DoFHandler<dim> &         mg_dof,
      const MGConstrainedDoFs *               mg_constrained_dofs,
      ElementInfo<Number> &                   elem_info,
      std::vector<std::vector<unsigned int>> &level_dof_indices,
      std::vector<std::vector<std::pair<unsigned int, unsigned int>>>
        &                        parent_child_connect,
      std::vector<unsigned int> &n_owned_level_cells,
      std::vector<std::vector<std::vector<unsigned short>>> &dirichlet_indices,
      std::vector<std::vector<Number>> &                     weights_on_refined,
      std::vector<std::vector<std::pair<unsigned int, unsigned int>>>
        &copy_indices_global_mine,
      MGLevelObject<LinearAlgebra::distributed::Vector<Number>>
        &ghosted_level_vector)
    {
      level_dof_indices.clear();
      parent_child_connect.clear();
      n_owned_level_cells.clear();
      dirichlet_indices.clear();
      weights_on_refined.clear();

      // we collect all child DoFs of a mother cell together. For faster
      // tensorized operations, we align the degrees of freedom
      // lexicographically. We distinguish FE_Q elements and FE_DGQ elements

      const ::Triangulation<dim> &tria = mg_dof.get_triangulation();

      // ---------------------------- 1. Extract 1D info about the finite
      // element step 1.1: create a 1D copy of the finite element from FETools
      // where we substitute the template argument
      AssertDimension(mg_dof.get_fe().n_base_elements(), 1);
      std::string fe_name = mg_dof.get_fe().base_element(0).get_name();
      {
        const std::size_t template_starts = fe_name.find_first_of('<');
        Assert(fe_name[template_starts + 1] ==
                 (dim == 1 ? '1' : (dim == 2 ? '2' : '3')),
               ExcInternalError());
        fe_name[template_starts + 1] = '1';
      }
      const std::unique_ptr<FiniteElement<1>> fe(
        FETools::get_fe_by_name<1, 1>(fe_name));

      setup_element_info(elem_info, *fe, mg_dof);


      // -------------- 2. Extract and match dof indices between child and
      // parent
      const unsigned int n_levels = tria.n_global_levels();
      level_dof_indices.resize(n_levels);
      parent_child_connect.resize(n_levels - 1);
      n_owned_level_cells.resize(n_levels - 1);
      std::vector<std::vector<unsigned int>> coarse_level_indices(n_levels - 1);
      for (unsigned int level = 0;
           level < std::min(tria.n_levels(), n_levels - 1);
           ++level)
        coarse_level_indices[level].resize(tria.n_raw_cells(level),
                                           numbers::invalid_unsigned_int);
      std::vector<types::global_dof_index> local_dof_indices(
        mg_dof.get_fe().dofs_per_cell);
      dirichlet_indices.resize(n_levels - 1);

      // We use the vectors stored ghosted_level_vector in the base class for
      // keeping ghosted transfer indices. To avoid keeping two very similar
      // vectors, we merge them here.
      if (ghosted_level_vector.max_level() != n_levels - 1)
        ghosted_level_vector.resize(0, n_levels - 1);

      for (unsigned int level = n_levels - 1; level > 0; --level)
        {
          unsigned int                         counter = 0;
          std::vector<types::global_dof_index> global_level_dof_indices;
          std::vector<types::global_dof_index> global_level_dof_indices_remote;
          std::vector<types::global_dof_index> ghosted_level_dofs;
          std::vector<types::global_dof_index> global_level_dof_indices_l0;
          std::vector<types::global_dof_index> ghosted_level_dofs_l0;

          // step 2.1: loop over the cells on the coarse side
          typename ::DoFHandler<dim>::cell_iterator cell,
            endc = mg_dof.end(level - 1);
          for (cell = mg_dof.begin(level - 1); cell != endc; ++cell)
            {
              // need to look into a cell if it has children and it is locally
              // owned
              if (!cell->has_children())
                continue;

              bool consider_cell = false;
              if (tria.locally_owned_subdomain() ==
                    numbers::invalid_subdomain_id ||
                  cell->level_subdomain_id() == tria.locally_owned_subdomain())
                consider_cell = true;

              // due to the particular way we store DoF indices (via children),
              // we also need to add the DoF indices for coarse cells where we
              // own at least one child
              bool cell_is_remote = !consider_cell;
              for (unsigned int c = 0;
                   c < GeometryInfo<dim>::max_children_per_cell;
                   ++c)
                if (cell->child(c)->level_subdomain_id() ==
                    tria.locally_owned_subdomain())
                  {
                    consider_cell = true;
                    break;
                  }

              if (!consider_cell)
                continue;

              // step 2.2: loop through children and append the dof indices to
              // the appropriate list. We need separate lists for the owned
              // coarse cell case (which will be part of
              // restriction/prolongation between level-1 and level) and the
              // remote case (which needs to store DoF indices for the
              // operations between level and level+1).
              AssertDimension(cell->n_children(),
                              GeometryInfo<dim>::max_children_per_cell);
              std::vector<types::global_dof_index> &next_indices =
                cell_is_remote ? global_level_dof_indices_remote :
                                 global_level_dof_indices;
              const std::size_t start_index = next_indices.size();
              next_indices.resize(start_index + elem_info.n_child_cell_dofs,
                                  numbers::invalid_dof_index);
              for (unsigned int c = 0;
                   c < GeometryInfo<dim>::max_children_per_cell;
                   ++c)
                {
                  if (cell_is_remote && cell->child(c)->level_subdomain_id() !=
                                          tria.locally_owned_subdomain())
                    continue;
                  cell->child(c)->get_mg_dof_indices(local_dof_indices);

                  replace(mg_constrained_dofs, level, local_dof_indices);

                  const IndexSet &owned_level_dofs =
                    mg_dof.locally_owned_mg_dofs(level);
                  for (unsigned int i = 0; i < local_dof_indices.size(); ++i)
                    if (!owned_level_dofs.is_element(local_dof_indices[i]))
                      ghosted_level_dofs.push_back(local_dof_indices[i]);

                  add_child_indices<dim>(c,
                                         fe->dofs_per_cell -
                                           fe->dofs_per_vertex,
                                         fe->degree,
                                         elem_info.lexicographic_numbering,
                                         local_dof_indices,
                                         &next_indices[start_index]);

                  // step 2.3 store the connectivity to the parent
                  if (cell->child(c)->has_children() &&
                      (tria.locally_owned_subdomain() ==
                         numbers::invalid_subdomain_id ||
                       cell->child(c)->level_subdomain_id() ==
                         tria.locally_owned_subdomain()))
                    {
                      const unsigned int child_index =
                        coarse_level_indices[level][cell->child(c)->index()];
                      AssertIndexRange(child_index,
                                       parent_child_connect[level].size());
                      unsigned int parent_index = counter;
                      // remote cells, i.e., cells where we work on a further
                      // level but are not treated on the current level, need to
                      // be placed at the end of the list; however, we do not
                      // yet know the exact position in the array, so shift
                      // their parent index by the number of cells so we can set
                      // the correct number after the end of this loop
                      if (cell_is_remote)
                        parent_index =
                          start_index / elem_info.n_child_cell_dofs +
                          tria.n_cells(level);
                      parent_child_connect[level][child_index] =
                        std::make_pair(parent_index, c);
                      AssertIndexRange(mg_dof.get_fe().dofs_per_cell,
                                       static_cast<unsigned short>(-1));

                      // set Dirichlet boundary conditions (as a list of
                      // constrained DoFs) for the child
                      if (mg_constrained_dofs != nullptr)
                        for (unsigned int i = 0;
                             i < mg_dof.get_fe().dofs_per_cell;
                             ++i)
                          if (mg_constrained_dofs->is_boundary_index(
                                level,
                                local_dof_indices
                                  [elem_info.lexicographic_numbering[i]]))
                            dirichlet_indices[level][child_index].push_back(i);
                    }
                }
              if (!cell_is_remote)
                {
                  AssertIndexRange(static_cast<unsigned int>(cell->index()),
                                   coarse_level_indices[level - 1].size());
                  coarse_level_indices[level - 1][cell->index()] = counter++;
                }

              // step 2.4: include indices for the coarsest cells. we still
              // insert the indices as if they were from a child in order to use
              // the same code (the coarsest level does not matter much in terms
              // of memory, so we gain in code simplicity)
              if (level == 1 && !cell_is_remote)
                {
                  cell->get_mg_dof_indices(local_dof_indices);

                  replace(mg_constrained_dofs, level - 1, local_dof_indices);

                  const IndexSet &owned_level_dofs_l0 =
                    mg_dof.locally_owned_mg_dofs(0);
                  for (unsigned int i = 0; i < local_dof_indices.size(); ++i)
                    if (!owned_level_dofs_l0.is_element(local_dof_indices[i]))
                      ghosted_level_dofs_l0.push_back(local_dof_indices[i]);

                  const std::size_t start_index =
                    global_level_dof_indices_l0.size();
                  global_level_dof_indices_l0.resize(
                    start_index + elem_info.n_child_cell_dofs,
                    numbers::invalid_dof_index);
                  add_child_indices<dim>(
                    0,
                    fe->dofs_per_cell - fe->dofs_per_vertex,
                    fe->degree,
                    elem_info.lexicographic_numbering,
                    local_dof_indices,
                    &global_level_dof_indices_l0[start_index]);

                  dirichlet_indices[0].emplace_back();
                  if (mg_constrained_dofs != nullptr)
                    for (unsigned int i = 0; i < mg_dof.get_fe().dofs_per_cell;
                         ++i)
                      if (mg_constrained_dofs->is_boundary_index(
                            0,
                            local_dof_indices[elem_info
                                                .lexicographic_numbering[i]]))
                        dirichlet_indices[0].back().push_back(i);
                }
            }

          // step 2.5: store information about the current level and prepare the
          // Dirichlet indices and parent-child relationship for the next
          // coarser level
          AssertDimension(counter * elem_info.n_child_cell_dofs,
                          global_level_dof_indices.size());
          n_owned_level_cells[level - 1] = counter;
          dirichlet_indices[level - 1].resize(counter);
          parent_child_connect[level - 1].resize(
            counter,
            std::make_pair(numbers::invalid_unsigned_int,
                           numbers::invalid_unsigned_int));

          // step 2.6: put the cells with remotely owned parent to the end of
          // the list (these are needed for the transfer from level to level+1
          // but not for the transfer from level-1 to level).
          if (level < n_levels - 1)
            for (std::vector<std::pair<unsigned int, unsigned int>>::iterator
                   i = parent_child_connect[level].begin();
                 i != parent_child_connect[level].end();
                 ++i)
              if (i->first >= tria.n_cells(level))
                {
                  i->first -= tria.n_cells(level);
                  i->first += counter;
                }

          // step 2.7: Initialize the ghosted vector
          const parallel::Triangulation<dim, dim> *ptria =
            (dynamic_cast<const parallel::Triangulation<dim, dim> *>(&tria));
          const MPI_Comm communicator =
            ptria != nullptr ? ptria->get_communicator() : MPI_COMM_SELF;

          reinit_ghosted_vector(mg_dof.locally_owned_mg_dofs(level),
                                ghosted_level_dofs,
                                communicator,
                                ghosted_level_vector[level],
                                copy_indices_global_mine[level]);

          copy_indices_to_mpi_local_numbers(
            *ghosted_level_vector[level].get_partitioner(),
            global_level_dof_indices,
            global_level_dof_indices_remote,
            level_dof_indices[level]);
          // step 2.8: Initialize the ghosted vector for level 0
          if (level == 1)
            {
              for (unsigned int i = 0; i < parent_child_connect[0].size(); ++i)
                parent_child_connect[0][i] = std::make_pair(i, 0U);

              reinit_ghosted_vector(mg_dof.locally_owned_mg_dofs(0),
                                    ghosted_level_dofs_l0,
                                    communicator,
                                    ghosted_level_vector[0],
                                    copy_indices_global_mine[0]);

              copy_indices_to_mpi_local_numbers(
                *ghosted_level_vector[0].get_partitioner(),
                global_level_dof_indices_l0,
                std::vector<types::global_dof_index>(),
                level_dof_indices[0]);
            }
        }

      // ---------------------- 3. compute weights to make restriction additive

      const unsigned int n_child_dofs_1d =
        fe->degree + 1 + fe->dofs_per_cell - fe->dofs_per_vertex;

      // get the valence of the individual components and compute the weights as
      // the inverse of the valence
      weights_on_refined.resize(n_levels - 1);
      for (unsigned int level = 1; level < n_levels; ++level)
        {
          ghosted_level_vector[level] = 0;
          for (unsigned int c = 0; c < n_owned_level_cells[level - 1]; ++c)
            for (unsigned int j = 0; j < elem_info.n_child_cell_dofs; ++j)
              ghosted_level_vector[level].local_element(
                level_dof_indices[level][elem_info.n_child_cell_dofs * c +
                                         j]) += Number(1.);
          ghosted_level_vector[level].compress(VectorOperation::add);
          ghosted_level_vector[level].update_ghost_values();

          std::vector<unsigned int> degree_to_3(n_child_dofs_1d);
          degree_to_3[0] = 0;
          for (unsigned int i = 1; i < n_child_dofs_1d - 1; ++i)
            degree_to_3[i] = 1;
          degree_to_3.back() = 2;

          // we only store 3^dim weights because all dofs on a line have the
          // same valence, and all dofs on a quad have the same valence.
          weights_on_refined[level - 1].resize(n_owned_level_cells[level - 1] *
                                               Utilities::fixed_power<dim>(3));
          for (unsigned int c = 0; c < n_owned_level_cells[level - 1]; ++c)
            for (unsigned int k = 0, m = 0; k < (dim > 2 ? n_child_dofs_1d : 1);
                 ++k)
              for (unsigned int j = 0; j < (dim > 1 ? n_child_dofs_1d : 1); ++j)
                {
                  unsigned int shift = 9 * degree_to_3[k] + 3 * degree_to_3[j];
                  for (unsigned int i = 0; i < n_child_dofs_1d; ++i, ++m)
                    weights_on_refined[level -
                                       1][c * Utilities::fixed_power<dim>(3) +
                                          shift + degree_to_3[i]] =
                      Number(1.) /
                      ghosted_level_vector[level].local_element(
                        level_dof_indices[level]
                                         [elem_info.n_child_cell_dofs * c + m]);
                }
        }
    }

  } // namespace MGTransfer
} // namespace internal

// Explicit instantiations

#include "mg_transfer_internal.inst"

DEAL_II_NAMESPACE_CLOSE