fe_series_fourier.cc

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// ---------------------------------------------------------------------
//
// Copyright (C) 2016 - 2021 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/numbers.h>
#include <deal.II/base/thread_management.h>
 
#include <deal.II/fe/fe_series.h>
 
#include <iostream>
 
 
DEAL_II_NAMESPACE_OPEN
 
namespace
{
  void
  set_k_vectors(Table<1, Tensor<1, 1>> &k_vectors, const unsigned int N)
  {
    k_vectors.reinit(TableIndices<1>(N));
    for (unsigned int i = 0; i < N; ++i)
      k_vectors(i)[0] = 2. * numbers::PI * i;
  }
 
  void
  set_k_vectors(Table<2, Tensor<1, 2>> &k_vectors, const unsigned int N)
  {
    k_vectors.reinit(TableIndices<2>(N, N));
    for (unsigned int i = 0; i < N; ++i)
      for (unsigned int j = 0; j < N; ++j)
        {
          k_vectors(i, j)[0] = 2. * numbers::PI * i;
          k_vectors(i, j)[1] = 2. * numbers::PI * j;
        }
  }
 
  void
  set_k_vectors(Table<3, Tensor<1, 3>> &k_vectors, const unsigned int N)
  {
    k_vectors.reinit(TableIndices<3>(N, N, N));
    for (unsigned int i = 0; i < N; ++i)
      for (unsigned int j = 0; j < N; ++j)
        for (unsigned int k = 0; k < N; ++k)
          {
            k_vectors(i, j, k)[0] = 2. * numbers::PI * i;
            k_vectors(i, j, k)[1] = 2. * numbers::PI * j;
            k_vectors(i, j, k)[2] = 2. * numbers::PI * k;
          }
  }
 
 
 
  template <int dim, int spacedim>
  std::complex<double>
  integrate(const FiniteElement<dim, spacedim> &fe,
            const Quadrature<dim> &             quadrature,
            const Tensor<1, dim> &              k_vector,
            const unsigned int                  j,
            const unsigned int                  component)
  {
    std::complex<double> sum = 0;
    for (unsigned int q = 0; q < quadrature.size(); ++q)
      {
        const Point<dim> &x_q = quadrature.point(q);
        sum += std::exp(std::complex<double>(0, 1) * (k_vector * x_q)) *
               fe.shape_value_component(j, x_q, component) *
               quadrature.weight(q);
      }
    return sum;
  }
 
 
 
  /*
   * Ensure that the transformation matrix for FiniteElement index
   * @p fe_index is calculated. If not, calculate it.
   */
  template <int spacedim>
  void
  ensure_existence(
    const std::vector<unsigned int> &              n_coefficients_per_direction,
    const hp::FECollection<1, spacedim> &          fe_collection,
    const hp::QCollection<1> &                     q_collection,
    const Table<1, Tensor<1, 1>> &                 k_vectors,
    const unsigned int                             fe,
    const unsigned int                             component,
    std::vector<FullMatrix<std::complex<double>>> &fourier_transform_matrices)
  {
    AssertIndexRange(fe, fe_collection.size());
 
    if (fourier_transform_matrices[fe].m() == 0)
      {
        fourier_transform_matrices[fe].reinit(
          n_coefficients_per_direction[fe],
          fe_collection[fe].n_dofs_per_cell());
 
        for (unsigned int k = 0; k < n_coefficients_per_direction[fe]; ++k)
          for (unsigned int j = 0; j < fe_collection[fe].n_dofs_per_cell(); ++j)
            fourier_transform_matrices[fe](k, j) = integrate(
              fe_collection[fe], q_collection[fe], k_vectors(k), j, component);
      }
  }
 
  template <int spacedim>
  void
  ensure_existence(
    const std::vector<unsigned int> &              n_coefficients_per_direction,
    const hp::FECollection<2, spacedim> &          fe_collection,
    const hp::QCollection<2> &                     q_collection,
    const Table<2, Tensor<1, 2>> &                 k_vectors,
    const unsigned int                             fe,
    const unsigned int                             component,
    std::vector<FullMatrix<std::complex<double>>> &fourier_transform_matrices)
  {
    AssertIndexRange(fe, fe_collection.size());
 
    if (fourier_transform_matrices[fe].m() == 0)
      {
        fourier_transform_matrices[fe].reinit(
          Utilities::fixed_power<2>(n_coefficients_per_direction[fe]),
          fe_collection[fe].n_dofs_per_cell());
 
        unsigned int k = 0;
        for (unsigned int k1 = 0; k1 < n_coefficients_per_direction[fe]; ++k1)
          for (unsigned int k2 = 0; k2 < n_coefficients_per_direction[fe];
               ++k2, ++k)
            for (unsigned int j = 0; j < fe_collection[fe].n_dofs_per_cell();
                 ++j)
              fourier_transform_matrices[fe](k, j) =
                integrate(fe_collection[fe],
                          q_collection[fe],
                          k_vectors(k1, k2),
                          j,
                          component);
      }
  }
 
  template <int spacedim>
  void
  ensure_existence(
    const std::vector<unsigned int> &              n_coefficients_per_direction,
    const hp::FECollection<3, spacedim> &          fe_collection,
    const hp::QCollection<3> &                     q_collection,
    const Table<3, Tensor<1, 3>> &                 k_vectors,
    const unsigned int                             fe,
    const unsigned int                             component,
    std::vector<FullMatrix<std::complex<double>>> &fourier_transform_matrices)
  {
    AssertIndexRange(fe, fe_collection.size());
 
    if (fourier_transform_matrices[fe].m() == 0)
      {
        fourier_transform_matrices[fe].reinit(
          Utilities::fixed_power<3>(n_coefficients_per_direction[fe]),
          fe_collection[fe].n_dofs_per_cell());
 
        unsigned int k = 0;
        for (unsigned int k1 = 0; k1 < n_coefficients_per_direction[fe]; ++k1)
          for (unsigned int k2 = 0; k2 < n_coefficients_per_direction[fe]; ++k2)
            for (unsigned int k3 = 0; k3 < n_coefficients_per_direction[fe];
                 ++k3, ++k)
              for (unsigned int j = 0; j < fe_collection[fe].n_dofs_per_cell();
                   ++j)
                fourier_transform_matrices[fe](k, j) =
                  integrate(fe_collection[fe],
                            q_collection[fe],
                            k_vectors(k1, k2, k3),
                            j,
                            component);
      }
  }
} // namespace
 
 
 
namespace FESeries
{
  template <int dim, int spacedim>
  Fourier<dim, spacedim>::Fourier(
    const std::vector<unsigned int> &      n_coefficients_per_direction,
    const hp::FECollection<dim, spacedim> &fe_collection,
    const hp::QCollection<dim> &           q_collection,
    const unsigned int                     component_)
    : n_coefficients_per_direction(n_coefficients_per_direction)
    , fe_collection(&fe_collection)
    , q_collection(q_collection)
    , fourier_transform_matrices(fe_collection.size())
    , component(component_ != numbers::invalid_unsigned_int ? component_ : 0)
  {
    Assert(n_coefficients_per_direction.size() == fe_collection.size() &&
             n_coefficients_per_direction.size() == q_collection.size(),
           ExcMessage("All parameters are supposed to have the same size."));
 
    if (fe_collection[0].n_components() > 1)
      Assert(
        component_ != numbers::invalid_unsigned_int,
        ExcMessage(
          "For vector-valued problems, you need to explicitly specify for "
          "which vector component you will want to do a Fourier decomposition "
          "by setting the 'component' argument of this constructor."));
 
    AssertIndexRange(component, fe_collection[0].n_components());
 
    const unsigned int max_n_coefficients_per_direction =
      *std::max_element(n_coefficients_per_direction.cbegin(),
                        n_coefficients_per_direction.cend());
    set_k_vectors(k_vectors, max_n_coefficients_per_direction);
 
    // reserve sufficient memory
    unrolled_coefficients.reserve(k_vectors.n_elements());
  }
 
 
 
  template <int dim, int spacedim>
  inline bool
  Fourier<dim, spacedim>::operator==(
    const Fourier<dim, spacedim> &fourier) const
  {
    return (
      (n_coefficients_per_direction == fourier.n_coefficients_per_direction) &&
      (*fe_collection == *(fourier.fe_collection)) &&
      (q_collection == fourier.q_collection) &&
      (k_vectors == fourier.k_vectors) &&
      (fourier_transform_matrices == fourier.fourier_transform_matrices) &&
      (component == fourier.component));
  }
 
 
 
  template <int dim, int spacedim>
  void
  Fourier<dim, spacedim>::precalculate_all_transformation_matrices()
  {
    Threads::TaskGroup<> task_group;
    for (unsigned int fe = 0; fe < fe_collection->size(); ++fe)
      task_group += Threads::new_task([&, fe]() {
        ensure_existence(n_coefficients_per_direction,
                         *fe_collection,
                         q_collection,
                         k_vectors,
                         fe,
                         component,
                         fourier_transform_matrices);
      });
 
    task_group.join_all();
  }
 
 
 
  template <int dim, int spacedim>
  unsigned int
  Fourier<dim, spacedim>::get_n_coefficients_per_direction(
    const unsigned int index) const
  {
    return n_coefficients_per_direction[index];
  }
 
 
 
  template <int dim, int spacedim>
  template <typename Number>
  void
  Fourier<dim, spacedim>::calculate(
    const Vector<Number> &       local_dof_values,
    const unsigned int           cell_active_fe_index,
    Table<dim, CoefficientType> &fourier_coefficients)
  {
    for (unsigned int d = 0; d < dim; ++d)
      AssertDimension(fourier_coefficients.size(d),
                      n_coefficients_per_direction[cell_active_fe_index]);
 
    ensure_existence(n_coefficients_per_direction,
                     *fe_collection,
                     q_collection,
                     k_vectors,
                     cell_active_fe_index,
                     component,
                     fourier_transform_matrices);
 
    const FullMatrix<CoefficientType> &matrix =
      fourier_transform_matrices[cell_active_fe_index];
 
    unrolled_coefficients.resize(Utilities::fixed_power<dim>(
      n_coefficients_per_direction[cell_active_fe_index]));
    std::fill(unrolled_coefficients.begin(),
              unrolled_coefficients.end(),
              CoefficientType(0.));
 
    Assert(unrolled_coefficients.size() == matrix.m(), ExcInternalError());
 
    Assert(local_dof_values.size() == matrix.n(),
           ExcDimensionMismatch(local_dof_values.size(), matrix.n()));
 
    for (unsigned int i = 0; i < unrolled_coefficients.size(); ++i)
      for (unsigned int j = 0; j < local_dof_values.size(); ++j)
        unrolled_coefficients[i] += matrix[i][j] * local_dof_values[j];
 
    fourier_coefficients.fill(unrolled_coefficients.begin());
  }
} // namespace FESeries
 
 
// explicit instantiations
#include "fe_series_fourier.inst"
 
DEAL_II_NAMESPACE_CLOSE