generators.cc

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// ------------------------------------------------------------------------
//
// SPDX-License-Identifier: LGPL-2.1-or-later
// Copyright (C) 2019 - 2023 by the deal.II authors
//
// This file is part of the deal.II library.
//
// Part of the source code is dual licensed under Apache-2.0 WITH
// LLVM-exception OR LGPL-2.1-or-later. Detailed license information
// governing the source code and code contributions can be found in
// LICENSE.md and CONTRIBUTING.md at the top level directory of deal.II.
//
// ------------------------------------------------------------------------
 
#include <deal.II/base/bounding_box.h>
#include <deal.II/base/geometry_info.h>
#include <deal.II/base/quadrature_lib.h>
#include <deal.II/base/signaling_nan.h>
 
#include <deal.II/dofs/dof_tools.h>
 
#include <deal.II/fe/fe_nothing.h>
#include <deal.II/fe/fe_values.h>
 
#include <deal.II/grid/filtered_iterator.h>
 
#include <deal.II/particles/generators.h>
 
#include <limits>
 
DEAL_II_NAMESPACE_OPEN
 
namespace Particles
{
  namespace Generators
  {
    namespace
    {
      template <int dim>
      DeclException1(
        ProbabilityFunctionNegative,
        Point<dim>,
        << "Your probability density function in the particle generator "
           "returned a negative value for the following position: "
        << arg1 << ". Please check your function expression.");
 
 
      // This function integrates the given probability density
      // function over all cells of the triangulation. For each
      // cell it stores the cumulative sum (of all previous
      // cells including the current cell) in a vector that is then
      // returned. Therefore the returned vector has as many entries
      // as active cells, the first entry being the integral over the
      // first cell, and the last entry the integral over the whole
      // locally owned domain. Cells that are not locally owned
      // simply store the same value as the cell before (equivalent
      // to assuming a probability density function value of 0).
      template <int dim, int spacedim = dim>
      std::vector<double>
      compute_local_cumulative_cell_weights(
        const Triangulation<dim, spacedim> &triangulation,
        const Mapping<dim, spacedim>       &mapping,
        const Function<spacedim>           &probability_density_function)
      {
        std::vector<double> cumulative_cell_weights(
          triangulation.n_active_cells());
        double cumulative_weight = 0.0;
 
        // Evaluate function at all cell midpoints
        const QMidpoint<dim> quadrature_formula;
 
        // In the simplest case we do not even need a FEValues object, because
        // using cell->center() and cell->measure() would be equivalent. This
        // fails however for higher-order mappings.
        FE_Nothing<dim, spacedim> alibi_finite_element;
        FEValues<dim, spacedim>   fe_values(mapping,
                                          alibi_finite_element,
                                          quadrature_formula,
                                          update_quadrature_points |
                                            update_JxW_values);
 
        // compute the integral weight
        for (const auto &cell : triangulation.active_cell_iterators())
          {
            if (cell->is_locally_owned())
              {
                fe_values.reinit(cell);
                const double quadrature_point_weight =
                  probability_density_function.value(
                    fe_values.get_quadrature_points()[0]);
 
                AssertThrow(quadrature_point_weight >= 0.0,
                            ProbabilityFunctionNegative<dim>(
                              quadrature_formula.point(0)));
 
                // get_cell_weight makes sure to return positive values
                cumulative_weight += quadrature_point_weight * fe_values.JxW(0);
              }
            cumulative_cell_weights[cell->active_cell_index()] =
              cumulative_weight;
          }
 
        return cumulative_cell_weights;
      }
 
 
 
      // This function generates a random position in the given cell and
      // returns the position and its coordinates in the reference cell. It
      // first tries to generate a random and uniformly distributed point in
      // real space, but if that fails (e.g. because the cell has a bad aspect
      // ratio) it reverts to generating a random point in the unit cell.
      template <int dim, int spacedim>
      std::pair<Point<spacedim>, Point<dim>>
      random_location_in_cell(
        const typename Triangulation<dim, spacedim>::active_cell_iterator &cell,
        const Mapping<dim, spacedim> &mapping,
        std::mt19937                 &random_number_generator)
      {
        Assert(cell->reference_cell().is_hyper_cube() == true,
               ExcNotImplemented());
 
        // Uniform distribution on the interval [0,1]. This
        // will be used to generate random particle locations.
        std::uniform_real_distribution<double> uniform_distribution_01(0, 1);
 
        const BoundingBox<spacedim> cell_bounding_box(cell->bounding_box());
        const std::pair<Point<spacedim>, Point<spacedim>> &cell_bounds(
          cell_bounding_box.get_boundary_points());
 
        // Generate random points in these bounds until one is within the cell
        // or we exceed the maximum number of attempts.
        const unsigned int n_attempts = 100;
        for (unsigned int i = 0; i < n_attempts; ++i)
          {
            Point<spacedim> position;
            for (unsigned int d = 0; d < spacedim; ++d)
              {
                position[d] = uniform_distribution_01(random_number_generator) *
                                (cell_bounds.second[d] - cell_bounds.first[d]) +
                              cell_bounds.first[d];
              }
 
            try
              {
                const Point<dim> reference_position =
                  mapping.transform_real_to_unit_cell(cell, position);
 
                if (cell->reference_cell().contains_point(reference_position))
                  return {position, reference_position};
              }
            catch (typename Mapping<dim>::ExcTransformationFailed &)
              {
                // The point is not in this cell. Do nothing, just try again.
              }
          }
 
        // If the above algorithm has not worked (e.g. because of badly
        // deformed cells), retry generating particles
        // randomly within the reference cell and then mapping it to to
        // real space. This is not generating a
        // uniform distribution in real space, but will always succeed.
        Point<dim> reference_position;
        for (unsigned int d = 0; d < dim; ++d)
          reference_position[d] =
            uniform_distribution_01(random_number_generator);
 
        const Point<spacedim> position =
          mapping.transform_unit_to_real_cell(cell, reference_position);
 
        return {position, reference_position};
      }
    } // namespace
 
 
 
    template <int dim, int spacedim>
    void
    regular_reference_locations(
      const Triangulation<dim, spacedim> &triangulation,
      const std::vector<Point<dim>>      &particle_reference_locations,
      ParticleHandler<dim, spacedim>     &particle_handler,
      const Mapping<dim, spacedim>       &mapping)
    {
      types::particle_index particle_index = 0;
      types::particle_index n_particles_to_generate =
        triangulation.n_active_cells() * particle_reference_locations.size();
 
#ifdef DEAL_II_WITH_MPI
      if (const auto tria =
            dynamic_cast<const parallel::TriangulationBase<dim, spacedim> *>(
              &triangulation))
        {
          n_particles_to_generate = tria->n_locally_owned_active_cells() *
                                    particle_reference_locations.size();
 
          // The local particle start index is the number of all particles
          // generated on lower MPI ranks.
          const int ierr = MPI_Exscan(&n_particles_to_generate,
                                      &particle_index,
                                      1,
                                      DEAL_II_PARTICLE_INDEX_MPI_TYPE,
                                      MPI_SUM,
                                      tria->get_mpi_communicator());
          AssertThrowMPI(ierr);
        }
#endif
 
      particle_handler.reserve(particle_handler.n_locally_owned_particles() +
                               n_particles_to_generate);
 
      for (const auto &cell : triangulation.active_cell_iterators() |
                                IteratorFilters::LocallyOwnedCell())
        {
          for (const auto &reference_location : particle_reference_locations)
            {
              const Point<spacedim> position_real =
                mapping.transform_unit_to_real_cell(cell, reference_location);
 
              particle_handler.insert_particle(position_real,
                                               reference_location,
                                               particle_index,
                                               cell);
              ++particle_index;
            }
        }
 
      particle_handler.update_cached_numbers();
    }
 
 
 
    template <int dim, int spacedim>
    Particle<dim, spacedim>
    random_particle_in_cell(
      const typename Triangulation<dim, spacedim>::active_cell_iterator &cell,
      const types::particle_index                                        id,
      std::mt19937                 &random_number_generator,
      const Mapping<dim, spacedim> &mapping)
    {
      const auto position_and_reference_position =
        random_location_in_cell(cell, mapping, random_number_generator);
      return Particle<dim, spacedim>(position_and_reference_position.first,
                                     position_and_reference_position.second,
                                     id);
    }
 
 
 
    template <int dim, int spacedim>
    ParticleIterator<dim, spacedim>
    random_particle_in_cell_insert(
      const typename Triangulation<dim, spacedim>::active_cell_iterator &cell,
      const types::particle_index                                        id,
      std::mt19937                   &random_number_generator,
      ParticleHandler<dim, spacedim> &particle_handler,
      const Mapping<dim, spacedim>   &mapping)
    {
      const auto position_and_reference_position =
        random_location_in_cell(cell, mapping, random_number_generator);
      return particle_handler.insert_particle(
        position_and_reference_position.first,
        position_and_reference_position.second,
        id,
        cell);
    }
 
 
 
    template <int dim, int spacedim>
    void
    probabilistic_locations(
      const Triangulation<dim, spacedim> &triangulation,
      const Function<spacedim>           &probability_density_function,
      const bool                          random_cell_selection,
      const types::particle_index         n_particles_to_create,
      ParticleHandler<dim, spacedim>     &particle_handler,
      const Mapping<dim, spacedim>       &mapping,
      const unsigned int                  random_number_seed)
    {
      unsigned int combined_seed = random_number_seed;
      if (const auto tria =
            dynamic_cast<const parallel::TriangulationBase<dim, spacedim> *>(
              &triangulation))
        {
          const unsigned int my_rank =
            Utilities::MPI::this_mpi_process(tria->get_mpi_communicator());
          combined_seed += my_rank;
        }
      std::mt19937 random_number_generator(combined_seed);
 
      types::particle_index start_particle_id(0);
      types::particle_index n_local_particles(0);
 
      std::vector<types::particle_index> particles_per_cell(
        triangulation.n_active_cells(), 0);
 
      // First determine how many particles to generate in which cell
      {
        // Get the local accumulated probabilities for every cell
        const std::vector<double> cumulative_cell_weights =
          compute_local_cumulative_cell_weights(triangulation,
                                                mapping,
                                                probability_density_function);
 
        // Sum the local integrals over all nodes
        double local_weight_integral = (cumulative_cell_weights.size() > 0) ?
                                         cumulative_cell_weights.back() :
                                         0.0;
 
 
        double local_start_weight     = numbers::signaling_nan<double>();
        double global_weight_integral = numbers::signaling_nan<double>();
 
        if (const auto tria =
              dynamic_cast<const parallel::TriangulationBase<dim, spacedim> *>(
                &triangulation))
          {
            std::tie(local_start_weight, global_weight_integral) =
              Utilities::MPI::partial_and_total_sum(
                local_weight_integral, tria->get_mpi_communicator());
          }
        else
          {
            local_start_weight     = 0;
            global_weight_integral = local_weight_integral;
          }
 
        AssertThrow(global_weight_integral > std::numeric_limits<double>::min(),
                    ExcMessage(
                      "The integral of the user prescribed probability "
                      "density function over the domain equals zero, "
                      "deal.II has no way to determine the cell of "
                      "generated particles. Please ensure that the "
                      "provided function is positive in at least a "
                      "part of the domain; also check the syntax of "
                      "the function."));
 
        // Calculate start id
        start_particle_id =
          std::llround(static_cast<double>(n_particles_to_create) *
                       local_start_weight / global_weight_integral);
 
        // Calculate number of local particles
        const types::particle_index end_particle_id =
          std::llround(static_cast<double>(n_particles_to_create) *
                       ((local_start_weight + local_weight_integral) /
                        global_weight_integral));
        n_local_particles = end_particle_id - start_particle_id;
 
        if (random_cell_selection)
          {
            // Uniform distribution on the interval [0,local_weight_integral).
            // This will be used to randomly select cells for all local
            // particles.
            std::uniform_real_distribution<double> uniform_distribution(
              0.0, local_weight_integral);
 
            // Loop over all particles to create locally and pick their cells
            for (types::particle_index current_particle_index = 0;
                 current_particle_index < n_local_particles;
                 ++current_particle_index)
              {
                // Draw the random number that determines the cell of the
                // particle
                const double random_weight =
                  uniform_distribution(random_number_generator);
 
                const std::vector<double>::const_iterator selected_cell =
                  std::lower_bound(cumulative_cell_weights.begin(),
                                   cumulative_cell_weights.end(),
                                   random_weight);
                const unsigned int cell_index =
                  std::distance(cumulative_cell_weights.begin(), selected_cell);
 
                ++particles_per_cell[cell_index];
              }
          }
        else
          {
            // Compute number of particles per cell according to the ratio
            // between their weight and the local weight integral
            types::particle_index particles_created = 0;
 
            for (const auto &cell : triangulation.active_cell_iterators() |
                                      IteratorFilters::LocallyOwnedCell())
              {
                const types::particle_index cumulative_particles_to_create =
                  std::llround(
                    static_cast<double>(n_local_particles) *
                    cumulative_cell_weights[cell->active_cell_index()] /
                    local_weight_integral);
 
                // Compute particles for this cell as difference between
                // number of particles that should be created including this
                // cell minus the number of particles already created.
                particles_per_cell[cell->active_cell_index()] =
                  cumulative_particles_to_create - particles_created;
                particles_created +=
                  particles_per_cell[cell->active_cell_index()];
              }
          }
      }
 
      // Now generate as many particles per cell as determined above
      {
        particle_handler.reserve(particle_handler.n_locally_owned_particles() +
                                 n_local_particles);
        unsigned int current_particle_index = start_particle_id;
 
        for (const auto &cell : triangulation.active_cell_iterators() |
                                  IteratorFilters::LocallyOwnedCell())
          {
            for (unsigned int i = 0;
                 i < particles_per_cell[cell->active_cell_index()];
                 ++i)
              {
                random_particle_in_cell_insert(cell,
                                               current_particle_index,
                                               random_number_generator,
                                               particle_handler,
                                               mapping);
 
                ++current_particle_index;
              }
          }
 
        particle_handler.update_cached_numbers();
      }
    }
 
 
 
    template <int dim, int spacedim>
    void
    dof_support_points(const DoFHandler<dim, spacedim> &dof_handler,
                       const std::vector<std::vector<BoundingBox<spacedim>>>
                                                      &global_bounding_boxes,
                       ParticleHandler<dim, spacedim> &particle_handler,
                       const Mapping<dim, spacedim>   &mapping,
                       const ComponentMask            &components,
                       const std::vector<std::vector<double>> &properties)
    {
      const auto &fe = dof_handler.get_fe();
 
      // Take care of components
      const ComponentMask mask =
        (components.size() == 0 ? ComponentMask(fe.n_components(), true) :
                                  components);
 
      const std::map<types::global_dof_index, Point<spacedim>>
        support_points_map =
          DoFTools::map_dofs_to_support_points(mapping, dof_handler, mask);
 
      // Generate the vector of points from the map
      // Memory is reserved for efficiency reasons
      std::vector<Point<spacedim>> support_points_vec;
      support_points_vec.reserve(support_points_map.size());
      for (const auto &element : support_points_map)
        support_points_vec.push_back(element.second);
 
      particle_handler.insert_global_particles(support_points_vec,
                                               global_bounding_boxes,
                                               properties);
    }
 
 
    template <int dim, int spacedim>
    void
    quadrature_points(
      const Triangulation<dim, spacedim> &triangulation,
      const Quadrature<dim>              &quadrature,
      // const std::vector<Point<dim>> &     particle_reference_locations,
      const std::vector<std::vector<BoundingBox<spacedim>>>
                                             &global_bounding_boxes,
      ParticleHandler<dim, spacedim>         &particle_handler,
      const Mapping<dim, spacedim>           &mapping,
      const std::vector<std::vector<double>> &properties)
    {
      const std::vector<Point<dim>> &particle_reference_locations =
        quadrature.get_points();
      std::vector<Point<spacedim>> points_to_generate;
      points_to_generate.reserve(particle_reference_locations.size() *
                                 triangulation.n_active_cells());
 
      //       Loop through cells and gather gauss points
      for (const auto &cell : triangulation.active_cell_iterators() |
                                IteratorFilters::LocallyOwnedCell())
        {
          for (const auto &reference_location : particle_reference_locations)
            {
              const Point<spacedim> position_real =
                mapping.transform_unit_to_real_cell(cell, reference_location);
              points_to_generate.push_back(position_real);
            }
        }
      particle_handler.insert_global_particles(points_to_generate,
                                               global_bounding_boxes,
                                               properties);
    }
  } // namespace Generators
} // namespace Particles
 
#include "generators.inst"
 
DEAL_II_NAMESPACE_CLOSE