particle_handler.cc

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// ---------------------------------------------------------------------
//
// Copyright (C) 2017 - 2020 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, redistribute
// it, and/or modify it under the terms of the GNU Lesser General
// Public License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
// The full text of the license can be found in the file LICENSE.md at
// the top level directory of deal.II.
//
// ---------------------------------------------------------------------
 
#include <deal.II/base/std_cxx14/memory.h>
 
#include <deal.II/grid/grid_tools.h>
#include <deal.II/grid/grid_tools_cache.h>
 
#include <deal.II/particles/particle_handler.h>
 
#include <utility>
 
DEAL_II_NAMESPACE_OPEN
 
namespace Particles
{
  namespace
  {
    template <int dim, int spacedim>
    std::vector<char>
    pack_particles(std::vector<Particle<dim, spacedim>> &particles)
    {
      std::vector<char> buffer;
 
      if (particles.size() == 0)
        return buffer;
 
      buffer.resize(particles.size() *
                    particles.front().serialized_size_in_bytes());
      void *current_data = buffer.data();
 
      for (const auto &particle : particles)
        {
          particle.write_data(current_data);
        }
 
      return buffer;
    }
 
    template <int dim, int spacedim>
    std::vector<Particle<dim, spacedim>>
    unpack_particles(
      const boost::iterator_range<std::vector<char>::const_iterator>
        &           data_range,
      PropertyPool &property_pool)
    {
      std::vector<Particle<dim, spacedim>> particles;
 
      if (data_range.empty())
        return particles;
 
      Particle<dim, spacedim> particle;
      particle.set_property_pool(property_pool);
      const unsigned int particle_size = particle.serialized_size_in_bytes();
 
      particles.reserve(data_range.size() / particle_size);
 
      const void *data = static_cast<const void *>(&(*data_range.begin()));
 
      while (data < &(*data_range.end()))
        {
          particles.emplace_back(data, &property_pool);
        }
 
      Assert(
        data == &(*data_range.end()),
        ExcMessage(
          "The particle data could not be deserialized successfully. "
          "Check that when deserializing the particles you expect the same "
          "number of properties that were serialized."));
 
      return particles;
    }
  } // namespace
 
  template <int dim, int spacedim>
  ParticleHandler<dim, spacedim>::ParticleHandler()
    : triangulation()
    , particles()
    , ghost_particles()
    , global_number_of_particles(0)
    , global_max_particles_per_cell(0)
    , next_free_particle_index(0)
    , property_pool(new PropertyPool(0))
    , size_callback()
    , store_callback()
    , load_callback()
    , handle(numbers::invalid_unsigned_int)
  {}
 
 
 
  template <int dim, int spacedim>
  ParticleHandler<dim, spacedim>::ParticleHandler(
    const Triangulation<dim, spacedim> &triangulation,
    const Mapping<dim, spacedim> &      mapping,
    const unsigned int                  n_properties)
    : triangulation(&triangulation, typeid(*this).name())
    , mapping(&mapping, typeid(*this).name())
    , particles()
    , ghost_particles()
    , global_number_of_particles(0)
    , global_max_particles_per_cell(0)
    , next_free_particle_index(0)
    , property_pool(new PropertyPool(n_properties))
    , size_callback()
    , store_callback()
    , load_callback()
    , handle(numbers::invalid_unsigned_int)
  {
    triangulation_cache =
      std_cxx14::make_unique<GridTools::Cache<dim, spacedim>>(triangulation,
                                                              mapping);
  }
 
 
 
  template <int dim, int spacedim>
  void
  ParticleHandler<dim, spacedim>::initialize(
    const Triangulation<dim, spacedim> &new_triangulation,
    const Mapping<dim, spacedim> &      new_mapping,
    const unsigned int                  n_properties)
  {
    triangulation = &new_triangulation;
    mapping       = &new_mapping;
 
    // Create the memory pool that will store all particle properties
    property_pool = std_cxx14::make_unique<PropertyPool>(n_properties);
 
    // Create the grid cache to cache the information about the triangulation
    // that is used to locate the particles into subdomains and cells
    triangulation_cache =
      std_cxx14::make_unique<GridTools::Cache<dim, spacedim>>(new_triangulation,
                                                              new_mapping);
  }
 
 
 
  template <int dim, int spacedim>
  void
  ParticleHandler<dim, spacedim>::clear()
  {
    clear_particles();
    global_number_of_particles    = 0;
    next_free_particle_index      = 0;
    global_max_particles_per_cell = 0;
  }
 
 
 
  template <int dim, int spacedim>
  void
  ParticleHandler<dim, spacedim>::clear_particles()
  {
    particles.clear();
  }
 
 
 
  template <int dim, int spacedim>
  void
  ParticleHandler<dim, spacedim>::update_cached_numbers()
  {
    types::particle_index locally_highest_index        = 0;
    unsigned int          local_max_particles_per_cell = 0;
    unsigned int          current_particles_per_cell   = 0;
    typename Triangulation<dim, spacedim>::active_cell_iterator current_cell =
      triangulation->begin_active();
 
    for (particle_iterator particle = begin(); particle != end(); ++particle)
      {
        locally_highest_index =
          std::max(locally_highest_index, particle->get_id());
 
        if (particle->get_surrounding_cell(*triangulation) != current_cell)
          {
            current_particles_per_cell = 0;
            current_cell = particle->get_surrounding_cell(*triangulation);
          }
 
        ++current_particles_per_cell;
        local_max_particles_per_cell =
          std::max(local_max_particles_per_cell, current_particles_per_cell);
      }
 
    if (const auto parallel_triangulation =
          dynamic_cast<const parallel::Triangulation<dim, spacedim> *>(
            &*triangulation))
      {
        global_number_of_particles = ::Utilities::MPI::sum(
          particles.size(), parallel_triangulation->get_communicator());
        next_free_particle_index =
          global_number_of_particles == 0 ?
            0 :
            ::Utilities::MPI::max(
              locally_highest_index,
              parallel_triangulation->get_communicator()) +
              1;
        global_max_particles_per_cell = ::Utilities::MPI::max(
          local_max_particles_per_cell,
          parallel_triangulation->get_communicator());
      }
    else
      {
        global_number_of_particles = particles.size();
        next_free_particle_index =
          global_number_of_particles == 0 ? 0 : locally_highest_index + 1;
        global_max_particles_per_cell = local_max_particles_per_cell;
      }
  }
 
 
 
  template <int dim, int spacedim>
  typename ParticleHandler<dim, spacedim>::particle_iterator
  ParticleHandler<dim, spacedim>::begin() const
  {
    return (const_cast<ParticleHandler<dim, spacedim> *>(this))->begin();
  }
 
 
 
  template <int dim, int spacedim>
  typename ParticleHandler<dim, spacedim>::particle_iterator
  ParticleHandler<dim, spacedim>::begin()
  {
    return particle_iterator(particles, particles.begin());
  }
 
 
 
  template <int dim, int spacedim>
  typename ParticleHandler<dim, spacedim>::particle_iterator
  ParticleHandler<dim, spacedim>::end() const
  {
    return (const_cast<ParticleHandler<dim, spacedim> *>(this))->end();
  }
 
 
 
  template <int dim, int spacedim>
  typename ParticleHandler<dim, spacedim>::particle_iterator
  ParticleHandler<dim, spacedim>::end()
  {
    return particle_iterator(particles, particles.end());
  }
 
 
 
  template <int dim, int spacedim>
  typename ParticleHandler<dim, spacedim>::particle_iterator
  ParticleHandler<dim, spacedim>::begin_ghost() const
  {
    return (const_cast<ParticleHandler<dim, spacedim> *>(this))->begin_ghost();
  }
 
 
 
  template <int dim, int spacedim>
  typename ParticleHandler<dim, spacedim>::particle_iterator
  ParticleHandler<dim, spacedim>::begin_ghost()
  {
    return particle_iterator(ghost_particles, ghost_particles.begin());
  }
 
 
 
  template <int dim, int spacedim>
  typename ParticleHandler<dim, spacedim>::particle_iterator
  ParticleHandler<dim, spacedim>::end_ghost() const
  {
    return (const_cast<ParticleHandler<dim, spacedim> *>(this))->end_ghost();
  }
 
 
 
  template <int dim, int spacedim>
  typename ParticleHandler<dim, spacedim>::particle_iterator
  ParticleHandler<dim, spacedim>::end_ghost()
  {
    return particle_iterator(ghost_particles, ghost_particles.end());
  }
 
 
 
  template <int dim, int spacedim>
  typename ParticleHandler<dim, spacedim>::particle_iterator_range
  ParticleHandler<dim, spacedim>::particles_in_cell(
    const typename Triangulation<dim, spacedim>::active_cell_iterator &cell)
    const
  {
    return (const_cast<ParticleHandler<dim, spacedim> *>(this))
      ->particles_in_cell(cell);
  }
 
 
 
  template <int dim, int spacedim>
  typename ParticleHandler<dim, spacedim>::particle_iterator_range
  ParticleHandler<dim, spacedim>::particles_in_cell(
    const typename Triangulation<dim, spacedim>::active_cell_iterator &cell)
  {
    const internal::LevelInd level_index =
      std::make_pair(cell->level(), cell->index());
 
    if (cell->is_ghost())
      {
        const auto particles_in_cell = ghost_particles.equal_range(level_index);
        return boost::make_iterator_range(
          particle_iterator(ghost_particles, particles_in_cell.first),
          particle_iterator(ghost_particles, particles_in_cell.second));
      }
 
    const auto particles_in_cell = particles.equal_range(level_index);
    return boost::make_iterator_range(
      particle_iterator(particles, particles_in_cell.first),
      particle_iterator(particles, particles_in_cell.second));
  }
 
 
 
  template <int dim, int spacedim>
  void
  ParticleHandler<dim, spacedim>::remove_particle(
    const ParticleHandler<dim, spacedim>::particle_iterator &particle)
  {
    particles.erase(particle->particle);
  }
 
 
 
  template <int dim, int spacedim>
  typename ParticleHandler<dim, spacedim>::particle_iterator
  ParticleHandler<dim, spacedim>::insert_particle(
    const Particle<dim, spacedim> &                                    particle,
    const typename Triangulation<dim, spacedim>::active_cell_iterator &cell)
  {
    typename std::multimap<internal::LevelInd,
                           Particle<dim, spacedim>>::iterator it =
      particles.insert(
        std::make_pair(internal::LevelInd(cell->level(), cell->index()),
                       particle));
 
    particle_iterator particle_it(particles, it);
    particle_it->set_property_pool(*property_pool);
 
    if (particle.has_properties())
      for (unsigned int n = 0; n < particle.get_properties().size(); ++n)
        particle_it->get_properties()[n] = particle.get_properties()[n];
 
    return particle_it;
  }
 
 
 
  template <int dim, int spacedim>
  void
  ParticleHandler<dim, spacedim>::insert_particles(
    const std::multimap<
      typename Triangulation<dim, spacedim>::active_cell_iterator,
      Particle<dim, spacedim>> &new_particles)
  {
    for (auto particle = new_particles.begin(); particle != new_particles.end();
         ++particle)
      particles.insert(
        particles.end(),
        std::make_pair(internal::LevelInd(particle->first->level(),
                                          particle->first->index()),
                       particle->second));
 
    update_cached_numbers();
  }
 
 
 
  template <int dim, int spacedim>
  void
  ParticleHandler<dim, spacedim>::insert_particles(
    const std::vector<Point<spacedim>> &positions)
  {
    update_cached_numbers();
 
    // Determine the starting particle index of this process, which
    // is the highest currently existing particle index plus the sum
    // of the number of newly generated particles of all
    // processes with a lower rank if in a parallel computation.
    const types::particle_index local_next_particle_index =
      get_next_free_particle_index();
    types::particle_index local_start_index = 0;
 
#ifdef DEAL_II_WITH_MPI
    if (const auto parallel_triangulation =
          dynamic_cast<const parallel::Triangulation<dim, spacedim> *>(
            &*triangulation))
      {
        types::particle_index particles_to_add_locally = positions.size();
        const int             ierr = MPI_Scan(&particles_to_add_locally,
                                  &local_start_index,
                                  1,
                                  DEAL_II_PARTICLE_INDEX_MPI_TYPE,
                                  MPI_SUM,
                                  parallel_triangulation->get_communicator());
        AssertThrowMPI(ierr);
        local_start_index -= particles_to_add_locally;
      }
#endif
 
    local_start_index += local_next_particle_index;
 
    GridTools::Cache<dim, spacedim> cache(*triangulation, *mapping);
    auto point_locations = GridTools::compute_point_locations(cache, positions);
 
    auto &cells           = std::get<0>(point_locations);
    auto &local_positions = std::get<1>(point_locations);
    auto &index_map       = std::get<2>(point_locations);
 
    if (cells.size() == 0)
      return;
 
    auto hint =
      particles.find(std::make_pair(cells[0]->level(), cells[0]->index()));
    for (unsigned int i = 0; i < cells.size(); ++i)
      {
        internal::LevelInd current_cell(cells[i]->level(), cells[i]->index());
        for (unsigned int p = 0; p < local_positions[i].size(); ++p)
          {
            hint = particles.insert(
              hint,
              std::make_pair(current_cell,
                             Particle<dim, spacedim>(positions[index_map[i][p]],
                                                     local_positions[i][p],
                                                     local_start_index +
                                                       index_map[i][p])));
          }
      }
 
    update_cached_numbers();
  }
 
 
 
  template <int dim, int spacedim>
  std::map<unsigned int, IndexSet>
  ParticleHandler<dim, spacedim>::insert_global_particles(
    const std::vector<Point<spacedim>> &positions,
    const std::vector<std::vector<BoundingBox<spacedim>>>
      &                                     global_bounding_boxes,
    const std::vector<std::vector<double>> &properties)
  {
    if (!properties.empty())
      {
        AssertDimension(properties.size(), positions.size());
#ifdef DEBUG
        for (const auto &p : properties)
          AssertDimension(p.size(), n_properties_per_particle());
#endif
      }
 
    const auto tria =
      dynamic_cast<const parallel::distributed::Triangulation<dim, spacedim> *>(
        &(*triangulation));
    const auto comm =
      (tria != nullptr ? tria->get_communicator() : MPI_COMM_WORLD);
 
    const auto n_mpi_processes = Utilities::MPI::n_mpi_processes(comm);
 
    GridTools::Cache<dim, spacedim> cache(*triangulation, *mapping);
 
    // Compute the global number of properties
    const auto n_global_properties =
      Utilities::MPI::sum(properties.size(), comm);
 
    // Gather the number of points per processor
    const auto n_particles_per_proc =
      Utilities::MPI::all_gather(comm, positions.size());
 
    // Calculate all starting points locally
    std::vector<unsigned int> particle_start_indices(n_mpi_processes);
 
    unsigned int particle_start_index = 0;
    for (unsigned int process = 0; process < particle_start_indices.size();
         ++process)
      {
        particle_start_indices[process] = particle_start_index;
        particle_start_index += n_particles_per_proc[process];
      }
 
    // Get all local information
    const auto cells_positions_and_index_maps =
      GridTools::distributed_compute_point_locations(cache,
                                                     positions,
                                                     global_bounding_boxes);
 
    // Unpack the information into several vectors:
    // All cells that contain at least one particle
    const auto &local_cells_containing_particles =
      std::get<0>(cells_positions_and_index_maps);
 
    // The reference position of every particle in the local part of the
    // triangulation.
    const auto &local_reference_positions =
      std::get<1>(cells_positions_and_index_maps);
    // The original index in the positions vector for each particle in the
    // local part of the triangulation
    const auto &original_indices_of_local_particles =
      std::get<2>(cells_positions_and_index_maps);
    // The real spatial position of every particle in the local part of the
    // triangulation.
    const auto &local_positions = std::get<3>(cells_positions_and_index_maps);
    // The MPI process that inserted each particle
    const auto &calling_process_indices =
      std::get<4>(cells_positions_and_index_maps);
 
    // Create the map of cpu to indices, indicating who sent us what
    // particle.
    std::map<unsigned int, IndexSet> original_process_to_local_particle_indices;
    for (unsigned int i_cell = 0;
         i_cell < local_cells_containing_particles.size();
         ++i_cell)
      {
        for (unsigned int i_particle = 0;
             i_particle < local_positions[i_cell].size();
             ++i_particle)
          {
            const unsigned int local_id_on_calling_process =
              original_indices_of_local_particles[i_cell][i_particle];
            const unsigned int calling_process =
              calling_process_indices[i_cell][i_particle];
 
            if (original_process_to_local_particle_indices.find(
                  calling_process) ==
                original_process_to_local_particle_indices.end())
              original_process_to_local_particle_indices.insert(
                {calling_process,
                 IndexSet(n_particles_per_proc[calling_process])});
 
            original_process_to_local_particle_indices[calling_process]
              .add_index(local_id_on_calling_process);
          }
      }
    for (auto &process_and_particle_indices :
         original_process_to_local_particle_indices)
      process_and_particle_indices.second.compress();
 
 
    // A map from mpi process to properties, ordered as in the IndexSet.
    // Notice that this ordering maybe different from the ordering in the
    // vectors above, since no local ordering is guaranteed by the
    // distribute_compute_point_locations() call.
    // This is only filled if n_global_properties is > 0
    std::map<unsigned int, std::vector<std::vector<double>>>
      locally_owned_properties_from_other_processes;
 
    if (n_global_properties > 0)
      {
        // Gather whom I sent my own particles to, to decide whom to send
        // the particle properties
        auto send_to_cpu = Utilities::MPI::some_to_some(
          comm, original_process_to_local_particle_indices);
 
        std::map<unsigned int, std::vector<std::vector<double>>>
          non_locally_owned_properties;
 
        // Prepare the vector of properties to send
        for (const auto &it : send_to_cpu)
          {
            std::vector<std::vector<double>> properties_to_send(
              it.second.n_elements(),
              std::vector<double>(n_properties_per_particle()));
            unsigned int index = 0;
            for (const auto &el : it.second)
              properties_to_send[index++] = properties[el];
            non_locally_owned_properties.insert({it.first, properties_to_send});
          }
 
        // Send the non locally owned properties to each mpi process
        // that needs them
        locally_owned_properties_from_other_processes =
          Utilities::MPI::some_to_some(comm, non_locally_owned_properties);
 
        AssertDimension(locally_owned_properties_from_other_processes.size(),
                        original_process_to_local_particle_indices.size());
      }
 
 
    // Create the multimap of local particles
    std::multimap<typename Triangulation<dim, spacedim>::active_cell_iterator,
                  Particle<dim, spacedim>>
      particles;
 
    // Now fill up the actual particles
    for (unsigned int i_cell = 0;
         i_cell < local_cells_containing_particles.size();
         ++i_cell)
      {
        for (unsigned int i_particle = 0;
             i_particle < local_positions[i_cell].size();
             ++i_particle)
          {
            const unsigned int local_id_on_calling_process =
              original_indices_of_local_particles[i_cell][i_particle];
            const unsigned int calling_process =
              calling_process_indices[i_cell][i_particle];
 
            const unsigned int particle_id =
              local_id_on_calling_process +
              particle_start_indices[calling_process];
 
            Particle<dim, spacedim> particle(
              local_positions[i_cell][i_particle],
              local_reference_positions[i_cell][i_particle],
              particle_id);
 
            if (n_global_properties > 0)
              {
                const unsigned int index_within_set =
                  original_process_to_local_particle_indices[calling_process]
                    .index_within_set(local_id_on_calling_process);
 
                const auto &this_particle_properties =
                  locally_owned_properties_from_other_processes
                    [calling_process][index_within_set];
 
                particle.set_property_pool(get_property_pool());
                particle.set_properties(this_particle_properties);
              }
 
            particles.emplace(local_cells_containing_particles[i_cell],
                              particle);
          }
      }
 
    this->insert_particles(particles);
 
    return original_process_to_local_particle_indices;
  }
 
 
 
  template <int dim, int spacedim>
  types::particle_index
  ParticleHandler<dim, spacedim>::n_global_particles() const
  {
    return global_number_of_particles;
  }
 
 
 
  template <int dim, int spacedim>
  types::particle_index
  ParticleHandler<dim, spacedim>::n_global_max_particles_per_cell() const
  {
    return global_max_particles_per_cell;
  }
 
 
 
  template <int dim, int spacedim>
  types::particle_index
  ParticleHandler<dim, spacedim>::n_locally_owned_particles() const
  {
    return particles.size();
  }
 
 
 
  template <int dim, int spacedim>
  unsigned int
  ParticleHandler<dim, spacedim>::n_properties_per_particle() const
  {
    return property_pool->n_properties_per_slot();
  }
 
 
 
  template <int dim, int spacedim>
  unsigned int
  ParticleHandler<dim, spacedim>::n_particles_in_cell(
    const typename Triangulation<dim, spacedim>::active_cell_iterator &cell)
    const
  {
    const internal::LevelInd found_cell =
      std::make_pair(cell->level(), cell->index());
 
    if (cell->is_locally_owned())
      return particles.count(found_cell);
    else if (cell->is_ghost())
      return ghost_particles.count(found_cell);
    else if (cell->is_artificial())
      AssertThrow(false, ExcInternalError());
 
    return 0;
  }
 
 
 
  template <int dim, int spacedim>
  types::particle_index
  ParticleHandler<dim, spacedim>::get_next_free_particle_index() const
  {
    return next_free_particle_index;
  }
 
 
 
  template <int dim, int spacedim>
  IndexSet
  ParticleHandler<dim, spacedim>::locally_relevant_ids() const
  {
    IndexSet set(get_next_free_particle_index());
    for (const auto &p : *this)
      set.add_index(p.get_id());
    set.compress();
    return set;
  }
 
 
 
  template <int dim, int spacedim>
  void
  ParticleHandler<dim, spacedim>::get_particle_positions(
    std::vector<Point<spacedim>> &positions,
    const bool                    add_to_output_vector)
  {
    // There should be one point per particle to gather
    AssertDimension(positions.size(), n_locally_owned_particles());
 
    unsigned int i = 0;
    for (auto it = begin(); it != end(); ++it, ++i)
      {
        if (add_to_output_vector)
          positions[i] = positions[i] + it->get_location();
        else
          positions[i] = it->get_location();
      }
  }
 
 
 
  template <int dim, int spacedim>
  void
  ParticleHandler<dim, spacedim>::set_particle_positions(
    const std::vector<Point<spacedim>> &new_positions,
    const bool                          displace_particles)
  {
    // There should be one point per particle to fix the new position
    AssertDimension(new_positions.size(), n_locally_owned_particles());
 
    unsigned int i = 0;
    for (auto it = begin(); it != end(); ++it, ++i)
      {
        if (displace_particles)
          it->set_location(it->get_location() + new_positions[i]);
        else
          it->set_location(new_positions[i]);
      }
    sort_particles_into_subdomains_and_cells();
  }
 
 
 
  template <int dim, int spacedim>
  void
  ParticleHandler<dim, spacedim>::set_particle_positions(
    const Function<spacedim> &function,
    const bool                displace_particles)
  {
    // The function should have sufficient components to displace the
    // particles
    AssertDimension(function.n_components, spacedim);
 
    Vector<double> new_position(spacedim);
    for (auto &particle : *this)
      {
        Point<spacedim> particle_location = particle.get_location();
        function.vector_value(particle_location, new_position);
        if (displace_particles)
          for (unsigned int d = 0; d < spacedim; ++d)
            particle_location[d] += new_position[d];
        else
          for (unsigned int d = 0; d < spacedim; ++d)
            particle_location[d] = new_position[d];
        particle.set_location(particle_location);
      }
    sort_particles_into_subdomains_and_cells();
  }
 
 
 
  template <int dim, int spacedim>
  PropertyPool &
  ParticleHandler<dim, spacedim>::get_property_pool() const
  {
    return *property_pool;
  }
 
 
 
  namespace
  {
    template <int dim>
    bool
    compare_particle_association(
      const unsigned int                 a,
      const unsigned int                 b,
      const Tensor<1, dim> &             particle_direction,
      const std::vector<Tensor<1, dim>> &center_directions)
    {
      const double scalar_product_a = center_directions[a] * particle_direction;
      const double scalar_product_b = center_directions[b] * particle_direction;
 
      // The function is supposed to return if a is before b. We are looking
      // for the alignment of particle direction and center direction,
      // therefore return if the scalar product of a is larger.
      return (scalar_product_a > scalar_product_b);
    }
  } // namespace
 
 
 
  template <int dim, int spacedim>
  void
  ParticleHandler<dim, spacedim>::sort_particles_into_subdomains_and_cells()
  {
    // TODO: The current algorithm only works for particles that are in
    // the local domain or in ghost cells, because it only knows the
    // subdomain_id of ghost cells, but not of artificial cells. This
    // can be extended using the distributed version of compute point
    // locations.
    // TODO: Extend this function to allow keeping particles on other
    // processes around (with an invalid cell).
 
    std::vector<particle_iterator> particles_out_of_cell;
    particles_out_of_cell.reserve(n_locally_owned_particles());
 
    // Now update the reference locations of the moved particles
    for (particle_iterator it = begin(); it != end(); ++it)
      {
        const typename Triangulation<dim, spacedim>::cell_iterator cell =
          it->get_surrounding_cell(*triangulation);
 
        try
          {
            const Point<dim> p_unit =
              mapping->transform_real_to_unit_cell(cell, it->get_location());
            if (GeometryInfo<dim>::is_inside_unit_cell(p_unit))
              {
                it->set_reference_location(p_unit);
              }
            else
              {
                // The particle has left the cell
                particles_out_of_cell.push_back(it);
              }
          }
        catch (typename Mapping<dim>::ExcTransformationFailed &)
          {
            // The particle has left the cell
            particles_out_of_cell.push_back(it);
          }
      }
 
    // There are three reasons why a particle is not in its old cell:
    // It moved to another cell, to another subdomain or it left the mesh.
    // Particles that moved to another cell are updated and stored inside the
    // sorted_particles vector, particles that moved to another domain are
    // collected in the moved_particles_domain vector. Particles that left
    // the mesh completely are ignored and removed.
    std::vector<std::pair<internal::LevelInd, Particle<dim, spacedim>>>
      sorted_particles;
    std::map<types::subdomain_id, std::vector<particle_iterator>>
      moved_particles;
    std::map<
      types::subdomain_id,
      std::vector<typename Triangulation<dim, spacedim>::active_cell_iterator>>
      moved_cells;
 
    // We do not know exactly how many particles are lost, exchanged between
    // domains, or remain on this process. Therefore we pre-allocate
    // approximate sizes for these vectors. If more space is needed an
    // automatic and relatively fast (compared to other parts of this
    // algorithm) re-allocation will happen.
    using vector_size = typename std::vector<particle_iterator>::size_type;
    sorted_particles.reserve(
      static_cast<vector_size>(particles_out_of_cell.size() * 1.25));
 
    std::set<types::subdomain_id> ghost_owners;
    if (const auto parallel_triangulation =
          dynamic_cast<const parallel::Triangulation<dim, spacedim> *>(
            &*triangulation))
      ghost_owners = parallel_triangulation->ghost_owners();
 
    for (const auto ghost_owner : ghost_owners)
      moved_particles[ghost_owner].reserve(
        static_cast<vector_size>(particles_out_of_cell.size() * 0.25));
    for (const auto ghost_owner : ghost_owners)
      moved_cells[ghost_owner].reserve(
        static_cast<vector_size>(particles_out_of_cell.size() * 0.25));
 
    {
      // Create a map from vertices to adjacent cells using grid cache
      std::vector<
        std::set<typename Triangulation<dim, spacedim>::active_cell_iterator>>
        vertex_to_cells = triangulation_cache->get_vertex_to_cell_map();
 
      // Create a corresponding map of vectors from vertex to cell center using
      // grid cache
      std::vector<std::vector<Tensor<1, spacedim>>> vertex_to_cell_centers =
        triangulation_cache->get_vertex_to_cell_centers_directions();
 
      std::vector<unsigned int> neighbor_permutation;
 
      // Find the cells that the particles moved to.
      typename std::vector<particle_iterator>::iterator
        it           = particles_out_of_cell.begin(),
        end_particle = particles_out_of_cell.end();
 
      for (; it != end_particle; ++it)
        {
          // The cell the particle is in
          Point<dim> current_reference_position;
          bool       found_cell = false;
 
          // Check if the particle is in one of the old cell's neighbors
          // that are adjacent to the closest vertex
          typename Triangulation<dim, spacedim>::active_cell_iterator
            current_cell = (*it)->get_surrounding_cell(*triangulation);
 
          const unsigned int closest_vertex =
            GridTools::find_closest_vertex_of_cell<dim, spacedim>(
              current_cell, (*it)->get_location());
          Tensor<1, spacedim> vertex_to_particle =
            (*it)->get_location() - current_cell->vertex(closest_vertex);
          vertex_to_particle /= vertex_to_particle.norm();
 
          const unsigned int closest_vertex_index =
            current_cell->vertex_index(closest_vertex);
          const unsigned int n_neighbor_cells =
            vertex_to_cells[closest_vertex_index].size();
 
          neighbor_permutation.resize(n_neighbor_cells);
          for (unsigned int i = 0; i < n_neighbor_cells; ++i)
            neighbor_permutation[i] = i;
 
          const auto cell_centers =
            vertex_to_cell_centers[closest_vertex_index];
          std::sort(neighbor_permutation.begin(),
                    neighbor_permutation.end(),
                    [&vertex_to_particle, &cell_centers](const unsigned int a,
                                                         const unsigned int b) {
                      return compare_particle_association(a,
                                                          b,
                                                          vertex_to_particle,
                                                          cell_centers);
                    });
 
          // Search all of the cells adjacent to the closest vertex of the
          // previous cell Most likely we will find the particle in them.
          for (unsigned int i = 0; i < n_neighbor_cells; ++i)
            {
              try
                {
                  typename std::set<typename Triangulation<dim, spacedim>::
                                      active_cell_iterator>::const_iterator
                    cell = vertex_to_cells[closest_vertex_index].begin();
 
                  std::advance(cell, neighbor_permutation[i]);
                  const Point<dim> p_unit =
                    mapping->transform_real_to_unit_cell(*cell,
                                                         (*it)->get_location());
                  if (GeometryInfo<dim>::is_inside_unit_cell(p_unit))
                    {
                      current_cell               = *cell;
                      current_reference_position = p_unit;
                      found_cell                 = true;
                      break;
                    }
                }
              catch (typename Mapping<dim>::ExcTransformationFailed &)
                {}
            }
 
          if (!found_cell)
            {
              // The particle is not in a neighbor of the old cell.
              // Look for the new cell in the whole local domain.
              // This case is rare.
              try
                {
                  const std::pair<const typename Triangulation<dim, spacedim>::
                                    active_cell_iterator,
                                  Point<dim>>
                    current_cell_and_position =
                      GridTools::find_active_cell_around_point<>(
                        *mapping, *triangulation, (*it)->get_location());
                  current_cell               = current_cell_and_position.first;
                  current_reference_position = current_cell_and_position.second;
                }
              catch (GridTools::ExcPointNotFound<spacedim> &)
                {
                  // We can find no cell for this particle. It has left the
                  // domain due to an integration error or an open boundary.
                  continue;
                }
            }
 
          // If we are here, we found a cell and reference position for this
          // particle
          (*it)->set_reference_location(current_reference_position);
 
          // Reinsert the particle into our domain if we own its cell.
          // Mark it for MPI transfer otherwise
          if (current_cell->is_locally_owned())
            {
              sorted_particles.push_back(
                std::make_pair(internal::LevelInd(current_cell->level(),
                                                  current_cell->index()),
                               (*it)->particle->second));
            }
          else
            {
              moved_particles[current_cell->subdomain_id()].push_back(*it);
              moved_cells[current_cell->subdomain_id()].push_back(current_cell);
            }
        }
    }
 
    // Sort the updated particles. This pre-sort speeds up inserting
    // them into particles to O(N) complexity.
    std::multimap<internal::LevelInd, Particle<dim, spacedim>>
      sorted_particles_map;
 
    // Exchange particles between processors if we have more than one process
#ifdef DEAL_II_WITH_MPI
    if (const auto parallel_triangulation =
          dynamic_cast<const parallel::Triangulation<dim, spacedim> *>(
            &*triangulation))
      {
        if (::Utilities::MPI::n_mpi_processes(
              parallel_triangulation->get_communicator()) > 1)
          send_recv_particles(moved_particles,
                              sorted_particles_map,
                              moved_cells);
      }
#endif
 
    sorted_particles_map.insert(sorted_particles.begin(),
                                sorted_particles.end());
 
    for (unsigned int i = 0; i < particles_out_of_cell.size(); ++i)
      remove_particle(particles_out_of_cell[i]);
 
    particles.insert(sorted_particles_map.begin(), sorted_particles_map.end());
    update_cached_numbers();
  }
 
 
 
  template <int dim, int spacedim>
  void
  ParticleHandler<dim, spacedim>::exchange_ghost_particles()
  {
    // Nothing to do in serial computations
    const auto parallel_triangulation =
      dynamic_cast<const parallel::Triangulation<dim, spacedim> *>(
        &*triangulation);
    if (parallel_triangulation != nullptr)
      {
        if (::Utilities::MPI::n_mpi_processes(
              parallel_triangulation->get_communicator()) == 1)
          return;
      }
    else
      return;
 
#ifdef DEAL_II_WITH_MPI
    // First clear the current ghost_particle information
    ghost_particles.clear();
 
    std::map<types::subdomain_id, std::vector<particle_iterator>>
      ghost_particles_by_domain;
 
    const std::set<types::subdomain_id> ghost_owners =
      parallel_triangulation->ghost_owners();
    for (const auto ghost_owner : ghost_owners)
      ghost_particles_by_domain[ghost_owner].reserve(
        static_cast<typename std::vector<particle_iterator>::size_type>(
          particles.size() * 0.25));
 
    std::vector<std::set<unsigned int>> vertex_to_neighbor_subdomain(
      triangulation->n_vertices());
 
    for (const auto &cell : triangulation->active_cell_iterators())
      {
        if (cell->is_ghost())
          for (const unsigned int v : GeometryInfo<dim>::vertex_indices())
            vertex_to_neighbor_subdomain[cell->vertex_index(v)].insert(
              cell->subdomain_id());
      }
 
    for (const auto &cell : triangulation->active_cell_iterators())
      {
        if (!cell->is_ghost())
          {
            std::set<unsigned int> cell_to_neighbor_subdomain;
            for (const unsigned int v : GeometryInfo<dim>::vertex_indices())
              {
                cell_to_neighbor_subdomain.insert(
                  vertex_to_neighbor_subdomain[cell->vertex_index(v)].begin(),
                  vertex_to_neighbor_subdomain[cell->vertex_index(v)].end());
              }
 
            if (cell_to_neighbor_subdomain.size() > 0)
              {
                const particle_iterator_range particle_range =
                  particles_in_cell(cell);
 
                for (const auto domain : cell_to_neighbor_subdomain)
                  {
                    for (typename particle_iterator_range::iterator particle =
                           particle_range.begin();
                         particle != particle_range.end();
                         ++particle)
                      ghost_particles_by_domain[domain].push_back(particle);
                  }
              }
          }
      }
 
    send_recv_particles(ghost_particles_by_domain, ghost_particles);
#endif
  }
 
 
 
#ifdef DEAL_II_WITH_MPI
  template <int dim, int spacedim>
  void
  ParticleHandler<dim, spacedim>::send_recv_particles(
    const std::map<types::subdomain_id, std::vector<particle_iterator>>
      &particles_to_send,
    std::multimap<internal::LevelInd, Particle<dim, spacedim>>
      &received_particles,
    const std::map<
      types::subdomain_id,
      std::vector<typename Triangulation<dim, spacedim>::active_cell_iterator>>
      &send_cells)
  {
    const auto parallel_triangulation =
      dynamic_cast<const parallel::Triangulation<dim, spacedim> *>(
        &*triangulation);
    Assert(
      parallel_triangulation,
      ExcMessage(
        "This function is only implemented for parallel::Triangulation objects."));
 
    // Determine the communication pattern
    const std::set<types::subdomain_id> ghost_owners =
      parallel_triangulation->ghost_owners();
    const std::vector<types::subdomain_id> neighbors(ghost_owners.begin(),
                                                     ghost_owners.end());
    const unsigned int                     n_neighbors = neighbors.size();
 
    if (send_cells.size() != 0)
      Assert(particles_to_send.size() == send_cells.size(), ExcInternalError());
 
    // If we do not know the subdomain this particle needs to be send to,
    // throw an error
    Assert(particles_to_send.find(numbers::artificial_subdomain_id) ==
             particles_to_send.end(),
           ExcInternalError());
 
    // TODO: Implement the shipping of particles to processes that are not
    // ghost owners of the local domain
    for (auto send_particles = particles_to_send.begin();
         send_particles != particles_to_send.end();
         ++send_particles)
      Assert(ghost_owners.find(send_particles->first) != ghost_owners.end(),
             ExcNotImplemented());
 
    unsigned int n_send_particles = 0;
    for (auto send_particles = particles_to_send.begin();
         send_particles != particles_to_send.end();
         ++send_particles)
      n_send_particles += send_particles->second.size();
 
    const unsigned int cellid_size = sizeof(CellId::binary_type);
 
    // Containers for the amount and offsets of data we will send
    // to other processors and the data itself.
    std::vector<unsigned int> n_send_data(n_neighbors, 0);
    std::vector<unsigned int> send_offsets(n_neighbors, 0);
    std::vector<char>         send_data;
 
    // Only serialize things if there are particles to be send.
    // We can not return early even if no particles
    // are send, because we might receive particles from other processes
    if (n_send_particles > 0)
      {
        // Allocate space for sending particle data
        const unsigned int particle_size =
          begin()->serialized_size_in_bytes() + cellid_size +
          (size_callback ? size_callback() : 0);
        send_data.resize(n_send_particles * particle_size);
        void *data = static_cast<void *>(&send_data.front());
 
        // Serialize the data sorted by receiving process
        for (unsigned int i = 0; i < n_neighbors; ++i)
          {
            send_offsets[i] = reinterpret_cast<std::size_t>(data) -
                              reinterpret_cast<std::size_t>(&send_data.front());
 
            for (unsigned int j = 0;
                 j < particles_to_send.at(neighbors[i]).size();
                 ++j)
              {
                // If no target cells are given, use the iterator information
                typename Triangulation<dim, spacedim>::active_cell_iterator
                  cell;
                if (send_cells.size() == 0)
                  cell =
                    particles_to_send.at(neighbors[i])[j]->get_surrounding_cell(
                      *triangulation);
                else
                  cell = send_cells.at(neighbors[i])[j];
 
                const CellId::binary_type cellid =
                  cell->id().template to_binary<dim>();
                memcpy(data, &cellid, cellid_size);
                data = static_cast<char *>(data) + cellid_size;
 
                particles_to_send.at(neighbors[i])[j]->write_data(data);
                if (store_callback)
                  data =
                    store_callback(particles_to_send.at(neighbors[i])[j], data);
              }
            n_send_data[i] = reinterpret_cast<std::size_t>(data) -
                             send_offsets[i] -
                             reinterpret_cast<std::size_t>(&send_data.front());
          }
      }
 
    // Containers for the data we will receive from other processors
    std::vector<unsigned int> n_recv_data(n_neighbors);
    std::vector<unsigned int> recv_offsets(n_neighbors);
 
    // Notify other processors how many particles we will send
    {
      const int mpi_tag = Utilities::MPI::internal::Tags::
        particle_handler_send_recv_particles_setup;
 
      std::vector<MPI_Request> n_requests(2 * n_neighbors);
      for (unsigned int i = 0; i < n_neighbors; ++i)
        {
          const int ierr = MPI_Irecv(&(n_recv_data[i]),
                                     1,
                                     MPI_UNSIGNED,
                                     neighbors[i],
                                     mpi_tag,
                                     parallel_triangulation->get_communicator(),
                                     &(n_requests[2 * i]));
          AssertThrowMPI(ierr);
        }
      for (unsigned int i = 0; i < n_neighbors; ++i)
        {
          const int ierr = MPI_Isend(&(n_send_data[i]),
                                     1,
                                     MPI_UNSIGNED,
                                     neighbors[i],
                                     mpi_tag,
                                     parallel_triangulation->get_communicator(),
                                     &(n_requests[2 * i + 1]));
          AssertThrowMPI(ierr);
        }
      const int ierr =
        MPI_Waitall(2 * n_neighbors, n_requests.data(), MPI_STATUSES_IGNORE);
      AssertThrowMPI(ierr);
    }
 
    // Determine how many particles and data we will receive
    unsigned int total_recv_data = 0;
    for (unsigned int neighbor_id = 0; neighbor_id < n_neighbors; ++neighbor_id)
      {
        recv_offsets[neighbor_id] = total_recv_data;
        total_recv_data += n_recv_data[neighbor_id];
      }
 
    // Set up the space for the received particle data
    std::vector<char> recv_data(total_recv_data);
 
    // Exchange the particle data between domains
    {
      std::vector<MPI_Request> requests(2 * n_neighbors);
      unsigned int             send_ops = 0;
      unsigned int             recv_ops = 0;
 
      const int mpi_tag = Utilities::MPI::internal::Tags::
        particle_handler_send_recv_particles_send;
 
      for (unsigned int i = 0; i < n_neighbors; ++i)
        if (n_recv_data[i] > 0)
          {
            const int ierr =
              MPI_Irecv(&(recv_data[recv_offsets[i]]),
                        n_recv_data[i],
                        MPI_CHAR,
                        neighbors[i],
                        mpi_tag,
                        parallel_triangulation->get_communicator(),
                        &(requests[send_ops]));
            AssertThrowMPI(ierr);
            send_ops++;
          }
 
      for (unsigned int i = 0; i < n_neighbors; ++i)
        if (n_send_data[i] > 0)
          {
            const int ierr =
              MPI_Isend(&(send_data[send_offsets[i]]),
                        n_send_data[i],
                        MPI_CHAR,
                        neighbors[i],
                        mpi_tag,
                        parallel_triangulation->get_communicator(),
                        &(requests[send_ops + recv_ops]));
            AssertThrowMPI(ierr);
            recv_ops++;
          }
      const int ierr =
        MPI_Waitall(send_ops + recv_ops, requests.data(), MPI_STATUSES_IGNORE);
      AssertThrowMPI(ierr);
    }
 
    // Put the received particles into the domain if they are in the
    // triangulation
    const void *recv_data_it = static_cast<const void *>(recv_data.data());
 
    while (reinterpret_cast<std::size_t>(recv_data_it) -
             reinterpret_cast<std::size_t>(recv_data.data()) <
           total_recv_data)
      {
        CellId::binary_type binary_cellid;
        memcpy(&binary_cellid, recv_data_it, cellid_size);
        const CellId id(binary_cellid);
        recv_data_it = static_cast<const char *>(recv_data_it) + cellid_size;
 
        const typename Triangulation<dim, spacedim>::active_cell_iterator cell =
          id.to_cell(*triangulation);
 
        typename std::multimap<internal::LevelInd,
                               Particle<dim, spacedim>>::iterator
          recv_particle = received_particles.insert(std::make_pair(
            internal::LevelInd(cell->level(), cell->index()),
            Particle<dim, spacedim>(recv_data_it, property_pool.get())));
 
        if (load_callback)
          recv_data_it =
            load_callback(particle_iterator(received_particles, recv_particle),
                          recv_data_it);
      }
 
    AssertThrow(recv_data_it == recv_data.data() + recv_data.size(),
                ExcMessage(
                  "The amount of data that was read into new particles "
                  "does not match the amount of data sent around."));
  }
#endif
 
 
 
  template <int dim, int spacedim>
  void
  ParticleHandler<dim, spacedim>::register_additional_store_load_functions(
    const std::function<std::size_t()> &                            size_callb,
    const std::function<void *(const particle_iterator &, void *)> &store_callb,
    const std::function<const void *(const particle_iterator &, const void *)>
      &load_callb)
  {
    size_callback  = size_callb;
    store_callback = store_callb;
    load_callback  = load_callb;
  }
 
 
 
  template <int dim, int spacedim>
  void
  ParticleHandler<dim, spacedim>::register_store_callback_function()
  {
    parallel::distributed::Triangulation<dim, spacedim>
      *non_const_triangulation =
        const_cast<parallel::distributed::Triangulation<dim, spacedim> *>(
          dynamic_cast<const parallel::distributed::Triangulation<dim, spacedim>
                         *>(&(*triangulation)));
    (void)non_const_triangulation;
 
    Assert(non_const_triangulation != nullptr, ::ExcNotImplemented());
 
#ifdef DEAL_II_WITH_P4EST
    // Only save and load particles if there are any, we might get here for
    // example if somebody created a ParticleHandler but generated 0
    // particles.
    update_cached_numbers();
 
    if (global_max_particles_per_cell > 0)
      {
        const auto callback_function =
          [this](const typename Triangulation<dim, spacedim>::cell_iterator
                   &cell_iterator,
                 const typename Triangulation<dim, spacedim>::CellStatus
                   cell_status) {
            return this->store_particles(cell_iterator, cell_status);
          };
 
        handle = non_const_triangulation->register_data_attach(
          callback_function, /*returns_variable_size_data=*/true);
      }
#endif
  }
 
 
 
  template <int dim, int spacedim>
  void
  ParticleHandler<dim, spacedim>::register_load_callback_function(
    const bool serialization)
  {
    // All particles have been stored, when we reach this point. Empty the
    // particle data.
    clear_particles();
 
    parallel::distributed::Triangulation<dim, spacedim>
      *non_const_triangulation =
        const_cast<parallel::distributed::Triangulation<dim, spacedim> *>(
          dynamic_cast<const parallel::distributed::Triangulation<dim, spacedim>
                         *>(&(*triangulation)));
    (void)non_const_triangulation;
 
    Assert(non_const_triangulation != nullptr, ::ExcNotImplemented());
 
#ifdef DEAL_II_WITH_P4EST
    // If we are resuming from a checkpoint, we first have to register the
    // store function again, to set the triangulation in the same state as
    // before the serialization. Only by this it knows how to deserialize the
    // data correctly. Only do this if something was actually stored.
    if (serialization && (global_max_particles_per_cell > 0))
      {
        const auto callback_function =
          [this](const typename Triangulation<dim, spacedim>::cell_iterator
                   &cell_iterator,
                 const typename Triangulation<dim, spacedim>::CellStatus
                   cell_status) {
            return this->store_particles(cell_iterator, cell_status);
          };
 
        handle = non_const_triangulation->register_data_attach(
          callback_function, /*returns_variable_size_data=*/true);
      }
 
    // Check if something was stored and load it
    if (handle != numbers::invalid_unsigned_int)
      {
        const auto callback_function =
          [this](
            const typename Triangulation<dim, spacedim>::cell_iterator
              &cell_iterator,
            const typename Triangulation<dim, spacedim>::CellStatus cell_status,
            const boost::iterator_range<std::vector<char>::const_iterator>
              &range_iterator) {
            this->load_particles(cell_iterator, cell_status, range_iterator);
          };
 
        non_const_triangulation->notify_ready_to_unpack(handle,
                                                        callback_function);
 
        // Reset handle and update global number of particles. The number
        // can change because of discarded or newly generated particles
        handle = numbers::invalid_unsigned_int;
        update_cached_numbers();
      }
#else
    (void)serialization;
#endif
  }
 
 
 
  template <int dim, int spacedim>
  std::vector<char>
  ParticleHandler<dim, spacedim>::store_particles(
    const typename Triangulation<dim, spacedim>::cell_iterator &cell,
    const typename Triangulation<dim, spacedim>::CellStatus     status) const
  {
    std::vector<Particle<dim, spacedim>> stored_particles_on_cell;
 
    switch (status)
      {
        case parallel::distributed::Triangulation<dim, spacedim>::CELL_PERSIST:
        case parallel::distributed::Triangulation<dim, spacedim>::CELL_REFINE:
          // If the cell persist or is refined store all particles of the
          // current cell.
          {
            unsigned int n_particles = 0;
 
            const internal::LevelInd level_index = {cell->level(),
                                                    cell->index()};
            const auto               particles_in_cell =
              (cell->is_ghost() ? ghost_particles.equal_range(level_index) :
                                  particles.equal_range(level_index));
 
            n_particles = n_particles_in_cell(cell);
            stored_particles_on_cell.reserve(n_particles);
 
            std::for_each(
              particles_in_cell.first,
              particles_in_cell.second,
              [&stored_particles_on_cell](
                const std::pair<internal::LevelInd, Particle<dim, spacedim>>
                  &particle) {
                stored_particles_on_cell.push_back(particle.second);
              });
 
            AssertDimension(n_particles, stored_particles_on_cell.size());
          }
          break;
 
        case parallel::distributed::Triangulation<dim, spacedim>::CELL_COARSEN:
          // If this cell is the parent of children that will be coarsened,
          // collect the particles of all children.
          {
            unsigned int n_particles = 0;
 
            for (unsigned int child_index = 0;
                 child_index < GeometryInfo<dim>::max_children_per_cell;
                 ++child_index)
              {
                const typename Triangulation<dim, spacedim>::cell_iterator
                  child = cell->child(child_index);
                n_particles += n_particles_in_cell(child);
              }
 
            stored_particles_on_cell.reserve(n_particles);
 
            for (unsigned int child_index = 0;
                 child_index < GeometryInfo<dim>::max_children_per_cell;
                 ++child_index)
              {
                const typename Triangulation<dim, spacedim>::cell_iterator
                                         child       = cell->child(child_index);
                const internal::LevelInd level_index = {child->level(),
                                                        child->index()};
                const auto               particles_in_cell =
                  (child->is_ghost() ?
                     ghost_particles.equal_range(level_index) :
                     particles.equal_range(level_index));
 
                std::for_each(
                  particles_in_cell.first,
                  particles_in_cell.second,
                  [&stored_particles_on_cell](
                    const std::pair<internal::LevelInd, Particle<dim, spacedim>>
                      &particle) {
                    stored_particles_on_cell.push_back(particle.second);
                  });
              }
 
            AssertDimension(n_particles, stored_particles_on_cell.size());
          }
          break;
 
        default:
          Assert(false, ExcInternalError());
          break;
      }
 
    return pack_particles(stored_particles_on_cell);
  }
 
  template <int dim, int spacedim>
  void
  ParticleHandler<dim, spacedim>::load_particles(
    const typename Triangulation<dim, spacedim>::cell_iterator &    cell,
    const typename Triangulation<dim, spacedim>::CellStatus         status,
    const boost::iterator_range<std::vector<char>::const_iterator> &data_range)
  {
    // We leave this container non-const to be able to `std::move`
    // its contents directly into the particles multimap later.
    std::vector<Particle<dim, spacedim>> loaded_particles_on_cell =
      unpack_particles<dim, spacedim>(data_range, *property_pool);
 
    // Update the reference to the current property pool for all particles.
    // This was not stored, because they might be transported across process
    // domains.
    for (auto &particle : loaded_particles_on_cell)
      particle.set_property_pool(*property_pool);
 
    switch (status)
      {
        case parallel::distributed::Triangulation<dim, spacedim>::CELL_PERSIST:
          {
            auto position_hint = particles.end();
            for (const auto &particle : loaded_particles_on_cell)
              {
                // Use std::multimap::emplace_hint to speed up insertion of
                // particles. This is a C++11 function, but not all compilers
                // that report a -std=c++11 (like gcc 4.6) implement it, so
                // require C++14 instead.
#ifdef DEAL_II_WITH_CXX14
                position_hint =
                  particles.emplace_hint(position_hint,
                                         std::make_pair(cell->level(),
                                                        cell->index()),
                                         std::move(particle));
#else
                position_hint =
                  particles.insert(position_hint,
                                   std::make_pair(std::make_pair(cell->level(),
                                                                 cell->index()),
                                                  std::move(particle)));
#endif
                // Move the hint position forward by one, i.e., for the next
                // particle. The 'hint' position will thus be right after the
                // one just inserted.
                ++position_hint;
              }
          }
          break;
 
        case parallel::distributed::Triangulation<dim, spacedim>::CELL_COARSEN:
          {
            typename std::multimap<internal::LevelInd,
                                   Particle<dim, spacedim>>::iterator
              position_hint = particles.end();
            for (auto &particle : loaded_particles_on_cell)
              {
                const Point<dim> p_unit =
                  mapping->transform_real_to_unit_cell(cell,
                                                       particle.get_location());
                particle.set_reference_location(p_unit);
                // Use std::multimap::emplace_hint to speed up insertion of
                // particles. This is a C++11 function, but not all compilers
                // that report a -std=c++11 (like gcc 4.6) implement it, so
                // require C++14 instead.
#ifdef DEAL_II_WITH_CXX14
                position_hint =
                  particles.emplace_hint(position_hint,
                                         std::make_pair(cell->level(),
                                                        cell->index()),
                                         std::move(particle));
#else
                position_hint =
                  particles.insert(position_hint,
                                   std::make_pair(std::make_pair(cell->level(),
                                                                 cell->index()),
                                                  std::move(particle)));
#endif
                // Move the hint position forward by one, i.e., for the next
                // particle. The 'hint' position will thus be right after the
                // one just inserted.
                ++position_hint;
              }
          }
          break;
 
        case parallel::distributed::Triangulation<dim, spacedim>::CELL_REFINE:
          {
            std::vector<
              typename std::multimap<internal::LevelInd,
                                     Particle<dim, spacedim>>::iterator>
              position_hints(GeometryInfo<dim>::max_children_per_cell);
            for (unsigned int child_index = 0;
                 child_index < GeometryInfo<dim>::max_children_per_cell;
                 ++child_index)
              {
                const typename Triangulation<dim, spacedim>::cell_iterator
                  child                     = cell->child(child_index);
                position_hints[child_index] = particles.upper_bound(
                  std::make_pair(child->level(), child->index()));
              }
 
            for (auto &particle : loaded_particles_on_cell)
              {
                for (unsigned int child_index = 0;
                     child_index < GeometryInfo<dim>::max_children_per_cell;
                     ++child_index)
                  {
                    const typename Triangulation<dim, spacedim>::cell_iterator
                      child = cell->child(child_index);
 
                    try
                      {
                        const Point<dim> p_unit =
                          mapping->transform_real_to_unit_cell(
                            child, particle.get_location());
                        if (GeometryInfo<dim>::is_inside_unit_cell(p_unit))
                          {
                            particle.set_reference_location(p_unit);
                            // Use std::multimap::emplace_hint to speed up
                            // insertion of particles. This is a C++11
                            // function, but not all compilers that report a
                            // -std=c++11 (like gcc 4.6) implement it, so
                            // require C++14 instead.
#ifdef DEAL_II_WITH_CXX14
                            position_hints[child_index] =
                              particles.emplace_hint(
                                position_hints[child_index],
                                std::make_pair(child->level(), child->index()),
                                std::move(particle));
#else
                            position_hints[child_index] = particles.insert(
                              position_hints[child_index],
                              std::make_pair(std::make_pair(child->level(),
                                                            child->index()),
                                             std::move(particle)));
#endif
                            // Move the hint position forward by one, i.e.,
                            // for the next particle. The 'hint' position will
                            // thus be right after the one just inserted.
                            ++position_hints[child_index];
                            break;
                          }
                      }
                    catch (typename Mapping<dim>::ExcTransformationFailed &)
                      {}
                  }
              }
          }
          break;
 
        default:
          Assert(false, ExcInternalError());
          break;
      }
  }
} // namespace Particles
 
#include "particle_handler.inst"
 
DEAL_II_NAMESPACE_CLOSE