mesh_adaptor.template.h

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//
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
// Copyright (C) 2024 - 2026 by the ryujin authors
//
 
#pragma once
 
#include "computing_timer.h"
#include "loop.h"
#include "mesh_adaptor.h"
#include "mpi_ensemble.h"
#include "simd.h"
 
#include <deal.II/base/array_view.h>
#include <deal.II/distributed/grid_refinement.h>
 
#include <boost/container/small_vector.hpp>
 
namespace ryujin
{
  template <typename HyperbolicDescription, int dim, typename Number>
  MeshAdaptor<HyperbolicDescription, dim, Number>::MeshAdaptor(
      const MPIEnsemble &mpi_ensemble,
      const OfflineData<dim, Number> &offline_data,
      const HyperbolicSystem &hyperbolic_system,
      const Interface::ParabolicSystem &parabolic_system,
      const MultiComponentVector<Number> &initial_precomputed,
      const ScalarVector<Number> &alpha,
      const std::string &subsection /*= "MeshAdaptor"*/)
      : ParameterAcceptor(subsection)
      , mpi_ensemble_(mpi_ensemble)
      , offline_data_(&offline_data)
      , selected_components_extractor_(offline_data,
                                       hyperbolic_system,
                                       parabolic_system,
                                       initial_precomputed,
                                       {"alpha"},
                                       {alpha})
      , need_mesh_adaptation_(false)
  {
    adaptation_strategy_ = AdaptationStrategy::smoothness_indicators;
    add_parameter("adaptation strategy",
                  adaptation_strategy_,
                  "The chosen adaptation strategy. Possible values are: global "
                  "refinement, random adaptation, smoothness indicators");
 
    marking_strategy_ = MarkingStrategy::fixed_threshold;
    add_parameter(
        "marking strategy",
        marking_strategy_,
        "The chosen marking strategy. Possible values are: fixed threshold.");
 
    time_point_selection_strategy_ =
        TimePointSelectionStrategy::simulation_cycle;
    add_parameter("time point selection strategy",
                  time_point_selection_strategy_,
                  "The chosen time point selection strategy. Possible values "
                  "are: fixed time points, simulation cycle");
 
    /* Options for various adaptation strategies: */
    enter_subsection("adaptation strategies");
    random_adaptation_mersenne_twister_seed_ = 42u;
    add_parameter("random adaptation: mersenne_twister_seed",
                  random_adaptation_mersenne_twister_seed_,
                  "Seed for 64bit Mersenne Twister used for random refinement");
 
    add_parameter(
        "smoothness indicators: quantities",
        smoothness_selected_quantities_,
        "List of conserved, primitive or precomputed quantities that will be "
        "used for constructing the smoothness indicator.");
 
    smoothness_local_global_ratio_ = 0.5;
    add_parameter(
        "smoothness indicators: local global ratio",
        smoothness_local_global_ratio_,
        "Ratio between local and global denominator value used for normalizing "
        "the smoothness indicator. A value of 1 indicates pure global "
        "normalization, a value of 0 indicates pure local normalization.");
 
    smoothness_min_cutoff_ = 0.0;
    add_parameter("smoothness indicators: min cutoff",
                  smoothness_min_cutoff_,
                  "minimal cutoff for the smoothness indicator: values below "
                  "this threshold will be set to the cutoff value.");
 
    smoothness_max_cutoff_ = 1.0e16;
    add_parameter("smoothness indicators: max cutoff",
                  smoothness_max_cutoff_,
                  "minimal cutoff for the smoothness indicator: values above "
                  "this threshold will be set to the cutoff value.");
 
    smoothness_widen_stencil_ = 15;
    add_parameter(
        "smoothness indicators: stencil size",
        smoothness_widen_stencil_,
        "Number of layers to widen the smoothness indicator stencil.");
    leave_subsection();
 
    /* Options for various marking strategies: */
 
    enter_subsection("marking strategies");
 
    coarsening_threshold_ = 0.25;
    add_parameter(
        "coarsening threshold",
        coarsening_threshold_,
        "Marking: normalized or absolute threshold for selecting cells for "
        "coarsening (used in \"fixed threshhold\" marking strategy).");
 
    refinement_threshold_ = 0.75;
    add_parameter(
        "refinement threshold",
        refinement_threshold_,
        "Marking: normalized or absolute threshold for selecting cells for "
        "refinement (used in \"fixed threshold\" marking strategy).");
 
    absolute_threshold_ = false;
    add_parameter("absolute threshold",
                  absolute_threshold_,
                  "Marking: if set to true use an absolute threshold for the "
                  "\"refinement threshold\" and \"coarsening threshold\" "
                  "values instead of a relative one. If this parameter is set "
                  "to false then the smoothness indicator is normalized into "
                  "the number range of [0., 1] and the threshold parameters "
                  "are also expected to be a value in this interval.");
 
    min_refinement_level_ = 0;
    add_parameter("minimal refinement level",
                  min_refinement_level_,
                  "Marking: minimal refinement level of cells that will be "
                  "maintained while coarsening cells.");
 
    max_refinement_level_ = 1000;
    add_parameter("maximal refinement level",
                  max_refinement_level_,
                  "Marking: maximal refinement level of cells that will be "
                  "maintained while refininig cells.");
    leave_subsection();
 
    /* Options for various time point selection strategies: */
 
    enter_subsection("time point selection strategies");
    adaptation_time_points_ = {};
    add_parameter("fixed time points",
                  adaptation_time_points_,
                  "List of time points in (simulation) time at which we will "
                  "perform a mesh adaptation cycle.");
 
    adaptation_cycle_interval_ = 10;
    add_parameter("simulation cycle: interval",
                  adaptation_cycle_interval_,
                  "The nth simulation cycle at which we will "
                  "perform mesh adapation.");
    leave_subsection();
 
    const auto call_back = [this] {
      /* Initialize Mersenne Twister with configured seed: */
      mersenne_twister_.seed(random_adaptation_mersenne_twister_seed_);
    };
 
    call_back();
    ParameterAcceptor::parse_parameters_call_back.connect(call_back);
  }
 
 
  template <typename HyperbolicDescription, int dim, typename Number>
  void MeshAdaptor<HyperbolicDescription, dim, Number>::prepare(const Number t)
  {
#ifdef DEBUG_OUTPUT
    std::cout << "MeshAdaptor<dim, Number>::prepare()" << std::endl;
#endif
 
    if (time_point_selection_strategy_ ==
        TimePointSelectionStrategy::fixed_time_points) {
      /* Remove outdated refinement timestamps: */
      const auto new_end = std::remove_if(
          adaptation_time_points_.begin(),
          adaptation_time_points_.end(),
          [&](const Number &t_refinement) { return (t > t_refinement); });
      adaptation_time_points_.erase(new_end, adaptation_time_points_.end());
    }
 
    selected_components_extractor_.prepare(smoothness_selected_quantities_);
 
    /* toggle mesh adaptation flag to off. */
    need_mesh_adaptation_ = false;
  }
 
 
  template <typename HyperbolicDescription, int dim, typename Number>
  void MeshAdaptor<HyperbolicDescription, dim, Number>::analyze(
      const StateVector<Number> &state_vector,
      const Number t,
      unsigned int cycle)
  {
#ifdef DEBUG_OUTPUT
    std::cout << "MeshAdaptor<dim, Number>::analyze()" << std::endl;
#endif
 
    /*
     * Decide whether we perform an adaptation cycle with the chosen time
     * point selection strategy:
     */
 
    switch (time_point_selection_strategy_) {
    case TimePointSelectionStrategy::fixed_time_points: {
      /* Remove all refinement points from the vector that lie in the past: */
      const auto new_end = std::remove_if( //
          adaptation_time_points_.begin(),
          adaptation_time_points_.end(),
          [&](const Number &t_refinement) {
            if (t < t_refinement)
              return false;
            need_mesh_adaptation_ = true;
            return true;
          });
      adaptation_time_points_.erase(new_end, adaptation_time_points_.end());
    } break;
 
    case TimePointSelectionStrategy::simulation_cycle: {
      /* check whether we reached a cycle interval: */
      if (cycle % adaptation_cycle_interval_ == 0)
        need_mesh_adaptation_ = true;
    } break;
 
    default:
      AssertThrow(false, dealii::ExcInternalError());
      __builtin_trap();
    }
 
    if (!need_mesh_adaptation_)
      return;
 
    /*
     * Some adaptation strategies require us to prepare some internal
     * data fields:
     */
 
    switch (adaptation_strategy_) {
    case AdaptationStrategy::global_refinement:
      /* do nothing */
      break;
 
    case AdaptationStrategy::random_adaptation:
      /* do nothing */
      break;
 
    case AdaptationStrategy::smoothness_indicators: {
      compute_smoothness_indicators(state_vector);
      break;
    }
 
    default:
      AssertThrow(false, dealii::ExcInternalError());
      __builtin_trap();
    }
  }
 
 
  template <typename HyperbolicDescription, int dim, typename Number>
  void MeshAdaptor<HyperbolicDescription, dim, Number>::
      populate_cell_indicators_with_random_values() const
  {
    std::generate(std::begin(indicators_), std::end(indicators_), [&]() {
      static std::uniform_real_distribution<double> distribution(0.0, 10.0);
      return distribution(mersenne_twister_);
    });
  }
 
 
  template <typename HyperbolicDescription, int dim, typename Number>
  void MeshAdaptor<HyperbolicDescription, dim, Number>::
      populate_cell_indicators_from_smoothness_indicators() const
  {
    const auto &scalar_partitioner = offline_data_->scalar_partitioner();
 
    /*
     * Distribute to cells by taking a cell-wise average:
     */
 
    std::vector<dealii::types::global_dof_index> local_dof_indices;
 
    const auto smoothness_indicators_view =
        smoothness_indicators_.template view<1>();
 
    const auto &dof_handler = offline_data_->dof_handler();
    for (const auto &cell : dof_handler.active_cell_iterators()) {
      if (!cell->is_locally_owned())
        continue;
 
      const unsigned int dofs_per_cell = cell->get_fe().n_dofs_per_cell();
      const auto scale = Number(1. / dofs_per_cell);
      local_dof_indices.resize(dofs_per_cell);
      cell->get_dof_indices(local_dof_indices);
 
      auto alpha_cell = Number(0.);
 
      for (unsigned int i = 0; i < dofs_per_cell; ++i) {
        const auto global_i = local_dof_indices[i];
        const auto local_i = scalar_partitioner->global_to_local(global_i);
        auto alpha_i =
            smoothness_indicators_view.template read_entry<Number>(local_i);
        alpha_cell += alpha_i;
      }
      alpha_cell *= scale;
 
      indicators_[cell->active_cell_index()] = static_cast<float>(alpha_cell);
    }
  }
 
 
  template <typename HyperbolicDescription, int dim, typename Number>
  void MeshAdaptor<HyperbolicDescription, dim, Number>::
      mark_cells_for_coarsening_and_refinement(
          dealii::Triangulation<dim> &triangulation [[maybe_unused]]) const
  {
    auto &discretization [[maybe_unused]] = offline_data_->discretization();
    Assert(&triangulation == &discretization.triangulation(),
           dealii::ExcInternalError());
 
    /*
     * Compute cell indicators with the chosen adaptation strategy:
     */
 
    switch (adaptation_strategy_) {
    case AdaptationStrategy::global_refinement: {
      /* Simply mark all cells for refinement and return: */
      for (auto &cell : triangulation.active_cell_iterators())
        cell->set_refine_flag();
      return;
    } break;
 
    case AdaptationStrategy::random_adaptation: {
      indicators_.reinit(triangulation.n_active_cells());
      populate_cell_indicators_with_random_values();
    } break;
 
    case AdaptationStrategy::smoothness_indicators: {
      indicators_.reinit(triangulation.n_active_cells());
      populate_cell_indicators_from_smoothness_indicators();
    } break;
 
    default:
      AssertThrow(false, dealii::ExcInternalError());
      __builtin_trap();
    }
 
    /*
     * Mark cells with chosen marking strategy:
     */
 
    switch (marking_strategy_) {
    case MarkingStrategy::fixed_threshold: {
 
      float inv_denominator = 1.f;
      float bias = 0.f;
 
      if (!absolute_threshold_) {
        /*
         * Normalize indicators to the interval [0., 1.]
         */
 
        float minimum = std::numeric_limits<float>::max();
        float maximum = 0.f;
        for (const auto &cell : triangulation.active_cell_iterators()) {
          if (!cell->is_locally_owned())
            continue;
          const auto indicator = indicators_[cell->active_cell_index()];
          minimum = std::min(minimum, indicator);
          maximum = std::max(maximum, indicator);
        }
        minimum = dealii::Utilities::MPI::min(
            minimum, mpi_ensemble_.ensemble_communicator());
        maximum = dealii::Utilities::MPI::max(
            maximum, mpi_ensemble_.ensemble_communicator());
 
        constexpr float eps = std::numeric_limits<float>::epsilon();
        // Ensure that if minimum == maximum we end up with 0.5 everywhere
        inv_denominator = 1.f / (maximum - minimum + 10.f * eps);
        bias = (minimum + 5.f * eps) * inv_denominator;
      }
 
      /*
       * And mark all cells according to threshold:
       */
 
      for (const auto &cell : triangulation.active_cell_iterators()) {
        if (!cell->is_locally_owned())
          continue;
 
        auto indicator = indicators_[cell->active_cell_index()];
        indicator = indicator * inv_denominator - bias;
        if (indicator < coarsening_threshold_)
          cell->set_coarsen_flag();
        else if (indicator > refinement_threshold_)
          cell->set_refine_flag();
      }
    } break;
 
    default:
      AssertThrow(false, dealii::ExcInternalError());
      __builtin_trap();
    }
 
    /*
     * Constrain refinement and coarsening to maximum and minimum
     * refinement levels:
     */
 
    if (triangulation.n_levels() > max_refinement_level_)
      for (const auto &cell :
           triangulation.active_cell_iterators_on_level(max_refinement_level_))
        cell->clear_refine_flag();
 
    for (const auto &cell :
         triangulation.active_cell_iterators_on_level(min_refinement_level_))
      cell->clear_coarsen_flag();
  }
 
 
  template <typename HyperbolicDescription, int dim, typename Number>
  void MeshAdaptor<HyperbolicDescription, dim, Number>::
      compute_smoothness_indicators(
          const StateVector<Number> &state_vector) const
  {
    const auto &affine_constraints = offline_data_->affine_constraints();
    const unsigned int n_internal = offline_data_->n_locally_internal();
    const unsigned int n_owned = offline_data_->n_locally_owned();
    const auto sparsity_simd_view =
        offline_data_->sparsity_pattern_simd().view();
    const auto betaij_matrix_view = offline_data_->betaij_matrix().view();
    using VA = dealii::VectorizedArray<Number>;
 
    /*
     * Extract selected quantities:
     */
 
    selected_components_extractor_.prepare_extraction(state_vector);
    auto quantities = selected_components_extractor_.view().extract();
 
    for (auto &it : quantities) {
      it.update_ghost_values();
      affine_constraints.distribute(it);
      it.update_ghost_values();
    }
 
    /*
     * Set up temporary vectors:
     */
 
    const unsigned int n_entries = quantities.size();
    const auto &scalar_partitioner = offline_data_->scalar_partitioner();
 
    /*
     * Ensure we have at least one entry in numerator and denominator
     * available. We use those for temporary storage.
     */
    std::vector<ScalarHostVector<Number>> numerator(std::max(1u, n_entries));
    std::vector<ScalarHostVector<Number>> denominator(std::max(1u, n_entries));
    for (auto &it : numerator)
      it.reinit(scalar_partitioner);
    for (auto &it : denominator)
      it.reinit(scalar_partitioner);
 
    /*
     * Commpute numerators and denominators for the smoothness indicators:
     */
 
    const auto body = [&](auto sentinel, unsigned int i) {
      using T = decltype(sentinel);
      const unsigned int stride_size = sparsity_simd_view.stride_of_row(i);
 
      /* Skip constrained degrees of freedom: */
      const unsigned int row_length = sparsity_simd_view.row_length(i);
      if (row_length == 1)
        return;
 
      boost::container::small_vector<T, 10> value_i(n_entries, T(0.));
      for (unsigned int k = 0; k < n_entries; ++k) {
        value_i[k] = read_entry<T>(quantities[k], i);
      }
 
      boost::container::small_vector<T, 10> numerator_i(n_entries, T(0.));
      boost::container::small_vector<T, 10> denominator_i(n_entries, T(0.));
 
      const unsigned int *js = sparsity_simd_view.columns(i);
      for (unsigned int col_idx = 0; col_idx < row_length;
           ++col_idx, js += stride_size) {
 
        /* Skip diagonal. */
        if (col_idx == 0)
          continue;
 
        const auto beta_ij =
            betaij_matrix_view.template read_entry<T>(i, col_idx);
 
        for (unsigned int k = 0; k < n_entries; ++k) {
          const auto value_j_k = read_entry<T>(quantities[k], js);
          numerator_i[k] += beta_ij * (value_j_k - value_i[k]);
          denominator_i[k] +=
              std::abs(beta_ij) * //
              std::max(std::abs(value_j_k), std::abs(value_i[k]));
        }
 
        for (unsigned int k = 0; k < n_entries; ++k) {
          write_entry<T>(numerator[k], numerator_i[k], i);
          write_entry<T>(denominator[k], denominator_i[k], i);
        }
      }
    };
 
    cpu_simd_loop<Number>("mesh_adaptor_1", body, 0, n_internal, n_owned);
 
    /*
     * Sum up and normalize the indicators and store the result in numerator[0]:
     */
 
    constexpr Number eps = std::numeric_limits<Number>::epsilon();
 
    std::vector<Number> denominator_global_maximum(n_entries);
    for (unsigned int k = 0; k < n_entries; ++k) {
      denominator_global_maximum[k] = dealii::Utilities::MPI::max(
          denominator[k].linfty_norm(), mpi_ensemble_.ensemble_communicator());
 
      denominator_global_maximum[k] =
          std::max(denominator_global_maximum[k], eps);
    }
 
    const auto body_normalize = [&](auto sentinel, unsigned int i) {
      using T = decltype(sentinel);
 
      /* Skip constrained degrees of freedom: */
      const unsigned int row_length = sparsity_simd_view.row_length(i);
      if (row_length == 1)
        return;
 
      auto alpha_i = T(0.);
      for (unsigned int k = 0; k < n_entries; ++k) {
        const auto numerator_i = read_entry<T>(numerator[k], i);
        const auto denominator_i = read_entry<T>(denominator[k], i);
 
        auto denominator =
            (Number(1.) - smoothness_local_global_ratio_) * denominator_i +
            smoothness_local_global_ratio_ * denominator_global_maximum[k];
        denominator = std::max(T(eps), denominator);
 
        alpha_i += std::abs(numerator_i) / denominator;
      }
 
      alpha_i = std::min(alpha_i, T(smoothness_max_cutoff_));
      alpha_i = std::max(alpha_i, T(smoothness_min_cutoff_));
      write_entry<T>(/*SIC!*/ numerator[0], alpha_i, i);
    };
 
    cpu_simd_loop<Number>(
        "mesh_adaptor_2", body_normalize, 0, n_internal, n_owned);
 
    /*
     * Widen indicators over stencil via max() operator:
     */
 
    const auto body_widen = [&](auto sentinel, unsigned int i) {
      using T = decltype(sentinel);
      const unsigned int stride_size = sparsity_simd_view.stride_of_row(i);
 
      /* Skip constrained degrees of freedom: */
      const unsigned int row_length = sparsity_simd_view.row_length(i);
      if (row_length == 1)
        return;
 
      auto alpha_i = read_entry<T>(numerator[0], i);
 
      const unsigned int *js = sparsity_simd_view.columns(i);
      for (unsigned int col_idx = 0; col_idx < row_length;
           ++col_idx, js += stride_size) {
 
        /* Skip diagonal. */
        if (col_idx == 0)
          continue;
 
        const auto alpha_j = read_entry<T>(numerator[0], js);
 
        alpha_i = std::max(alpha_i, alpha_j);
      }
 
      write_entry<T>(/*SIC!*/ denominator[0], alpha_i, i);
    };
 
    for (unsigned int cycle = 0; cycle < smoothness_widen_stencil_; ++cycle) {
      numerator[0].update_ghost_values();
      cpu_simd_loop<Number>(
          "mesh_adaptor_3", body_widen, 0, n_internal, n_owned);
      numerator[0] = /*SIC!*/ denominator[0];
    }
 
    numerator[0].update_ghost_values();
    affine_constraints.distribute(numerator[0]);
 
    /*
     * Insert result into smoothness_indicators_:
     */
 
    smoothness_indicators_.reinit_with_scalar_partitioner(scalar_partitioner,
                                                          1);
    const auto smoothness_indicators_view =
        smoothness_indicators_.template view<1>();
    smoothness_indicators_view.insert_component(numerator[0], 0);
    smoothness_indicators_view.update_ghost_values();
  }
} // namespace ryujin