solution_projection_between_triangulations.h

/*  ______________________________________________________________________
 *
 *  ExaDG - High-Order Discontinuous Galerkin for the Exa-Scale
 *
 *  Copyright (C) 2025 by the ExaDG authors
 *
 *  This program is free software: you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation, either version 3 of the License, or
 *  (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with this program. If not, see <https://www.gnu.org/licenses/>.
 *  ______________________________________________________________________
 */
 
#ifndef EXADG_OPERATORS_SOLUTION_PROJECTION_BETWEEN_TRIANGULATIONS_H_
#define EXADG_OPERATORS_SOLUTION_PROJECTION_BETWEEN_TRIANGULATIONS_H_
 
// C/C++
#include <algorithm>
 
// deal.II
#include <deal.II/base/conditional_ostream.h>
#include <deal.II/base/mpi_remote_point_evaluation.h>
#include <deal.II/base/timer.h>
#include <deal.II/matrix_free/fe_point_evaluation.h>
#include <deal.II/matrix_free/matrix_free.h>
#include <deal.II/numerics/vector_tools.h>
 
// ExaDG
#include <exadg/grid/grid_data.h>
#include <exadg/matrix_free/integrators.h>
#include <exadg/matrix_free/matrix_free_data.h>
#include <exadg/operators/inverse_mass_operator.h>
#include <exadg/operators/inverse_mass_parameters.h>
#include <exadg/operators/mapping_flags.h>
#include <exadg/operators/quadrature.h>
#include <exadg/postprocessor/write_output.h>
 
namespace ExaDG
{
namespace GridToGridProjection
{
// Parameters controlling the grid-to-grid projection.
template<int dim>
struct GridToGridProjectionData
{
  GridToGridProjectionData()
    : rpe_data(),
      solver_data(SolverData(1e3, 1e-20, 1e-6, LinearSolver::CG)),
      preconditioner(PreconditionerMass::PointJacobi),
      amg_data(AMGData()),
      additional_quadrature_points(1)
  {
  }
 
  void
  print(dealii::ConditionalOStream const & pcout) const
  {
    print_parameter(pcout, "RPE tolerance", rpe_data.tolerance);
    print_parameter(pcout, "RPE enforce unique mapping", rpe_data.enforce_unique_mapping);
    print_parameter(pcout, "RPE rtree level", rpe_data.rtree_level);
 
    // These parameters play only a role if an iterative scheme is used for projection.
    // That is for `InverseMassType != InverseMassType::MatrixfreeOperator` determined at runtime.
    solver_data.print(pcout);
    print_parameter(pcout, "Preconditioner", preconditioner);
    amg_data.print(pcout);
  }
 
  typename dealii::Utilities::MPI::RemotePointEvaluation<dim>::AdditionalData rpe_data;
  SolverData                                                                  solver_data;
  PreconditionerMass                                                          preconditioner;
  AMGData                                                                     amg_data;
 
  // Number of additional integration points used for sampling the source grid.
  // The default `additional_quadrature_points = 1` considers `fe_degree + 1` quadrature points in
  // 1D using the `fe_degree` of the target grid's finite element.
  unsigned int additional_quadrature_points;
};

template<int dim, int n_components, typename Number>
std::vector<dealii::Point<dim>>
collect_integration_points(
  dealii::MatrixFree<dim, Number, dealii::VectorizedArray<Number>> const & matrix_free,
  unsigned int const                                                       dof_index,
  unsigned int const                                                       quad_index)
{
  CellIntegrator<dim, n_components, Number> fe_eval(matrix_free, dof_index, quad_index);
 
  // Conservative estimate for the number of points.
  std::vector<dealii::Point<dim>> integration_points;
  integration_points.reserve(
    matrix_free.get_dof_handler(dof_index).get_triangulation().n_active_cells() *
    fe_eval.n_q_points);
 
  for(unsigned int cell_batch_idx = 0; cell_batch_idx < matrix_free.n_cell_batches();
      ++cell_batch_idx)
  {
    fe_eval.reinit(cell_batch_idx);
    for(const unsigned int q : fe_eval.quadrature_point_indices())
    {
      dealii::Point<dim, dealii::VectorizedArray<Number>> const cell_batch_points =
        fe_eval.quadrature_point(q);
      for(unsigned int i = 0; i < dealii::VectorizedArray<Number>::size(); ++i)
      {
        dealii::Point<dim> p;
        for(unsigned int d = 0; d < dim; ++d)
        {
          p[d] = cell_batch_points[d][i];
        }
        integration_points.push_back(p);
      }
    }
  }
 
  return integration_points;
}

template<int dim, int n_components, typename Number, typename VectorType>
VectorType
assemble_projection_rhs(
  dealii::MatrixFree<dim, Number, dealii::VectorizedArray<Number>> const & matrix_free,
  std::vector<
    typename dealii::FEPointEvaluation<n_components, dim, dim, Number>::value_type> const &
                     values_source_in_q_points_target,
  unsigned int const dof_index,
  unsigned int const quad_index)
{
  VectorType system_rhs;
  matrix_free.initialize_dof_vector(system_rhs, dof_index);
 
  CellIntegrator<dim, n_components, Number> fe_eval(matrix_free, dof_index, quad_index);
 
  unsigned int idx_q_point = 0;
 
  for(unsigned int cell_batch_idx = 0; cell_batch_idx < matrix_free.n_cell_batches();
      ++cell_batch_idx)
  {
    fe_eval.reinit(cell_batch_idx);
    for(unsigned int const q : fe_eval.quadrature_point_indices())
    {
      dealii::Tensor<1, n_components, dealii::VectorizedArray<Number>> tmp;
 
      for(unsigned int i = 0; i < dealii::VectorizedArray<Number>::size(); ++i)
      {
        typename dealii::FEPointEvaluation<n_components, dim, dim, Number>::value_type const
          values = values_source_in_q_points_target[idx_q_point];
 
        // Increment index into `values_source_in_q_points_target`, meaning that the sequence of
        // function values in integration points need to match the particular sequence here.
        ++idx_q_point;
 
        if constexpr(n_components == 1)
        {
          tmp[0][i] = values;
        }
        else
        {
          for(unsigned int c = 0; c < n_components; ++c)
          {
            tmp[c][i] = values[c];
          }
        }
      }
 
      fe_eval.submit_value(tmp, q);
    }
    fe_eval.integrate(dealii::EvaluationFlags::values);
    fe_eval.distribute_local_to_global(system_rhs);
  }
  system_rhs.compress(dealii::VectorOperation::add);
 
  return system_rhs;
}

template<int dim, typename Number, int n_components, typename VectorType>
void
project_vectors(
  std::shared_ptr<dealii::Mapping<dim> const> const &                      source_mapping,
  dealii::DoFHandler<dim> const &                                          source_dof_handler,
  std::vector<VectorType *> const &                                        source_vectors,
  dealii::MatrixFree<dim, Number, dealii::VectorizedArray<Number>> const & target_matrix_free,
  std::vector<VectorType *> const &                                        target_vectors,
  unsigned int const                                                       dof_index,
  unsigned int const                                                       quad_index,
  GridToGridProjectionData<dim> const &                                    data)
{
  // Setup inverse mass operator.
  InverseMassOperatorData<Number> inverse_mass_operator_data;
  inverse_mass_operator_data.dof_index                 = dof_index;
  inverse_mass_operator_data.quad_index                = quad_index;
  inverse_mass_operator_data.parameters.preconditioner = data.preconditioner;
  inverse_mass_operator_data.parameters.solver_data    = data.solver_data;
  inverse_mass_operator_data.parameters.amg_data       = data.amg_data;
 
  const bool cartesian_or_affine_mapping =
    std::all_of(target_matrix_free.get_mapping_info().cell_type.begin(),
                target_matrix_free.get_mapping_info().cell_type.end(),
                [](auto g) {
                  return g <= dealii::internal::MatrixFreeFunctions::GeometryType::affine;
                });
  inverse_mass_operator_data.parameters.implementation_type =
    InverseMassOperatorData<Number>::get_optimal_inverse_mass_type(
      target_matrix_free.get_dof_handler(dof_index).get_fe(), cartesian_or_affine_mapping);
 
  InverseMassOperator<dim, n_components, Number> inverse_mass_operator;
  inverse_mass_operator.initialize(target_matrix_free, inverse_mass_operator_data);
 
  dealii::Utilities::MPI::RemotePointEvaluation<dim> rpe_source(data.rpe_data);
 
  // The sequence of integration points follows from the sequence of points as encountered during
  // cell batch loop.
  std::vector<dealii::Point<dim>> integration_points_target =
    collect_integration_points<dim, n_components, Number>(target_matrix_free,
                                                          dof_index,
                                                          quad_index);
 
  rpe_source.reinit(integration_points_target,
                    source_dof_handler.get_triangulation(),
                    *source_mapping);
 
  if(not rpe_source.all_points_found())
  {
    write_points_in_dummy_triangulation(
      integration_points_target, "./", "points_all", 0, source_dof_handler.get_mpi_communicator());
 
    std::vector<dealii::Point<dim>> points_not_found;
    points_not_found.reserve(integration_points_target.size());
    for(unsigned int i = 0; i < integration_points_target.size(); ++i)
    {
      if(not rpe_source.point_found(i))
      {
        points_not_found.push_back(integration_points_target[i]);
      }
    }
 
    write_points_in_dummy_triangulation(
      points_not_found, "./", "points_not_found", 0, source_dof_handler.get_mpi_communicator());
 
    AssertThrow(
      rpe_source.all_points_found(),
      dealii::ExcMessage(
        "Could not interpolate source grid vector in target grid. "
        "Points exported to `./points_all_points.pvtu` and `./points_not_found_points.pvtu`"));
  }
 
  // Loop over vectors and project.
  for(unsigned int i = 0; i < target_vectors.size(); ++i)
  {
    // Evaluate the source vector at the target integration points.
    VectorType const & source_vector = *source_vectors.at(i);
    source_vector.update_ghost_values();
 
    std::vector<
      typename dealii::FEPointEvaluation<n_components, dim, dim, Number>::value_type> const
      values_source_in_q_points_target = dealii::VectorTools::point_values<n_components>(
        rpe_source, source_dof_handler, source_vector, dealii::VectorTools::EvaluationFlags::avg);
 
    // Assemble right-hand side vector for the projection.
    VectorType system_rhs = assemble_projection_rhs<dim, n_components, Number, VectorType>(
      target_matrix_free, values_source_in_q_points_target, dof_index, quad_index);
 
    // Solve linear system starting from zero initial guess.
    VectorType sol;
    sol.reinit(system_rhs, false /* omit_zeroing_entries */);
 
    inverse_mass_operator.apply(sol, system_rhs);
 
    // Copy solution to target vector.
    *target_vectors[i] = sol;
  }
}

template<int dim, typename Number, typename VectorType>
void
do_grid_to_grid_projection(
  std::shared_ptr<dealii::Mapping<dim> const> const &  source_mapping,
  std::vector<dealii::DoFHandler<dim> const *> const & source_dof_handlers,
  std::vector<std::vector<VectorType *>> const &       source_vectors_per_dof_handler,
  std::vector<dealii::DoFHandler<dim> const *> const & target_dof_handlers,
  dealii::MatrixFree<dim, Number, dealii::VectorizedArray<Number>> const & target_matrix_free,
  std::vector<std::vector<VectorType *>> & target_vectors_per_dof_handler,
  GridToGridProjectionData<dim> const &    data)
{
  // Check input dimensions.
  AssertThrow(source_vectors_per_dof_handler.size() == source_dof_handlers.size(),
              dealii::ExcMessage("First dimension of source vector of vectors "
                                 "has to match source DoFHandler count."));
  AssertThrow(target_vectors_per_dof_handler.size() == target_dof_handlers.size(),
              dealii::ExcMessage("First dimension of target vector of vectors "
                                 "has to match target DoFHandler count."));
  AssertThrow(source_dof_handlers.size() == target_dof_handlers.size(),
              dealii::ExcMessage("Target and source DoFHandler counts have to match"));
  AssertThrow(source_vectors_per_dof_handler.size() > 0,
              dealii::ExcMessage("Vector of source vectors empty."));
  for(unsigned int i = 0; i < source_vectors_per_dof_handler.size(); ++i)
  {
    AssertThrow(source_vectors_per_dof_handler[i].size() ==
                  target_vectors_per_dof_handler.at(i).size(),
                dealii::ExcMessage("Vectors of source and target vectors need to have same size."));
  }
 
  // Project vectors per `dealii::DoFHandler`.
  for(unsigned int i = 0; i < target_dof_handlers.size(); ++i)
  {
    unsigned int const n_components = target_dof_handlers[i]->get_fe().n_components();
    if(n_components == 1)
    {
      project_vectors<dim, Number, 1 /* n_components */, VectorType>(
        source_mapping,
        *source_dof_handlers.at(i),
        source_vectors_per_dof_handler.at(i),
        target_matrix_free,
        target_vectors_per_dof_handler.at(i),
        i /* dof_index */,
        i /* quad_index */,
        data);
    }
    else if(n_components == dim)
    {
      project_vectors<dim, Number, dim /* n_components */, VectorType>(
        source_mapping,
        *source_dof_handlers.at(i),
        source_vectors_per_dof_handler.at(i),
        target_matrix_free,
        target_vectors_per_dof_handler.at(i),
        i /* dof_index */,
        i /* quad_index */,
        data);
    }
    else if(n_components == dim + 2)
    {
      project_vectors<dim, Number, dim + 2 /* n_components */, VectorType>(
        source_mapping,
        *source_dof_handlers.at(i),
        source_vectors_per_dof_handler.at(i),
        target_matrix_free,
        target_vectors_per_dof_handler.at(i),
        i /* dof_index */,
        i /* quad_index */,
        data);
    }
    else
    {
      AssertThrow(n_components == 1 or n_components == dim,
                  dealii::ExcMessage("The requested number of components is not"
                                     "supported in `grid_to_grid_projection()`."));
    }
  }
}

template<int dim, typename Number, typename VectorType>
void
grid_to_grid_projection(
  std::shared_ptr<dealii::Mapping<dim> const> const &  source_mapping,
  std::vector<dealii::DoFHandler<dim> const *> const & source_dof_handlers,
  std::vector<std::vector<VectorType *>> const &       source_vectors_per_dof_handler,
  std::shared_ptr<dealii::Mapping<dim> const> const &  target_mapping,
  std::vector<dealii::DoFHandler<dim> const *> const & target_dof_handlers,
  std::vector<std::vector<VectorType *>> &             target_vectors_per_dof_handler,
  GridToGridProjectionData<dim> const &                data)
{
  // Setup a single `dealii::MatrixFree` object with multiple `dealii::DoFHandler`s.
  MatrixFreeData<dim, Number> target_matrix_free_data;
 
  MappingFlags mapping_flags;
  mapping_flags.cells =
    dealii::update_quadrature_points | dealii::update_values | dealii::update_JxW_values;
  target_matrix_free_data.append_mapping_flags(mapping_flags);
 
  dealii::AffineConstraints<Number> empty_constraints;
  empty_constraints.clear();
  empty_constraints.close();
  for(unsigned int i = 0; i < target_dof_handlers.size(); ++i)
  {
    target_matrix_free_data.insert_dof_handler(target_dof_handlers[i], std::to_string(i));
    target_matrix_free_data.insert_constraint(&empty_constraints, std::to_string(i));
 
    ElementType element_type = get_element_type(target_dof_handlers[i]->get_triangulation());
 
    std::shared_ptr<dealii::Quadrature<dim>> quadrature = create_quadrature<dim>(
      element_type, target_dof_handlers[i]->get_fe().degree + data.additional_quadrature_points);
 
    target_matrix_free_data.insert_quadrature(*quadrature, std::to_string(i));
  }
 
  dealii::MatrixFree<dim, Number, dealii::VectorizedArray<Number>> target_matrix_free;
 
  target_matrix_free.reinit(*target_mapping,
                            target_matrix_free_data.get_dof_handler_vector(),
                            target_matrix_free_data.get_constraint_vector(),
                            target_matrix_free_data.get_quadrature_vector(),
                            target_matrix_free_data.data);
 
  do_grid_to_grid_projection<dim, Number, VectorType>(source_mapping,
                                                      source_dof_handlers,
                                                      source_vectors_per_dof_handler,
                                                      target_dof_handlers,
                                                      target_matrix_free,
                                                      target_vectors_per_dof_handler,
                                                      data);
}
 
} // namespace GridToGridProjection
} // namespace ExaDG
 
#endif /* EXADG_OPERATORS_SOLUTION_PROJECTION_BETWEEN_TRIANGULATIONS_H_ */