mapping_q.h

Go to the documentation of this file.

// ---------------------------------------------------------------------
//
// Copyright (C) 2000 - 2022 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.
//
// ---------------------------------------------------------------------
 
#ifndef dealii_mapping_q_h
#define dealii_mapping_q_h
 
 
#include <deal.II/base/config.h>
 
#include <deal.II/base/derivative_form.h>
#include <deal.II/base/polynomial.h>
#include <deal.II/base/quadrature_lib.h>
#include <deal.II/base/table.h>
#include <deal.II/base/vectorization.h>
 
#include <deal.II/fe/mapping.h>
 
#include <deal.II/grid/tria_iterator.h>
 
#include <deal.II/matrix_free/shape_info.h>
#include <deal.II/matrix_free/tensor_product_kernels.h>
 
#include <array>
#include <cmath>
 
DEAL_II_NAMESPACE_OPEN
 
#ifndef DOXYGEN
template <int, int>
class MappingQCache;
#endif
 
 
 
template <int dim, int spacedim = dim>
class MappingQ : public Mapping<dim, spacedim>
{
public:
  MappingQ(const unsigned int polynomial_degree);
 
  DEAL_II_DEPRECATED_EARLY
  MappingQ(const unsigned int polynomial_degree,
           const bool         use_mapping_q_on_all_cells);
 
  MappingQ(const MappingQ<dim, spacedim> &mapping);
 
  // for documentation, see the Mapping base class
  virtual std::unique_ptr<Mapping<dim, spacedim>>
  clone() const override;
 
  unsigned int
  get_degree() const;
 
  virtual bool
  preserves_vertex_locations() const override;
 
  // for documentation, see the Mapping base class
  virtual BoundingBox<spacedim>
  get_bounding_box(const typename Triangulation<dim, spacedim>::cell_iterator
                     &cell) const override;
 
  virtual bool
  is_compatible_with(const ReferenceCell &reference_cell) const override;
 
  // for documentation, see the Mapping base class
  virtual Point<spacedim>
  transform_unit_to_real_cell(
    const typename Triangulation<dim, spacedim>::cell_iterator &cell,
    const Point<dim> &p) const override;
 
  // for documentation, see the Mapping base class
  virtual Point<dim>
  transform_real_to_unit_cell(
    const typename Triangulation<dim, spacedim>::cell_iterator &cell,
    const Point<spacedim> &p) const override;
 
  // for documentation, see the Mapping base class
  virtual void
  transform_points_real_to_unit_cell(
    const typename Triangulation<dim, spacedim>::cell_iterator &cell,
    const ArrayView<const Point<spacedim>> &                    real_points,
    const ArrayView<Point<dim>> &unit_points) const override;
 
  // for documentation, see the Mapping base class
  virtual void
  transform(const ArrayView<const Tensor<1, dim>> &                  input,
            const MappingKind                                        kind,
            const typename Mapping<dim, spacedim>::InternalDataBase &internal,
            const ArrayView<Tensor<1, spacedim>> &output) const override;
 
  // for documentation, see the Mapping base class
  virtual void
  transform(const ArrayView<const DerivativeForm<1, dim, spacedim>> &input,
            const MappingKind                                        kind,
            const typename Mapping<dim, spacedim>::InternalDataBase &internal,
            const ArrayView<Tensor<2, spacedim>> &output) const override;
 
  // for documentation, see the Mapping base class
  virtual void
  transform(const ArrayView<const Tensor<2, dim>> &                  input,
            const MappingKind                                        kind,
            const typename Mapping<dim, spacedim>::InternalDataBase &internal,
            const ArrayView<Tensor<2, spacedim>> &output) const override;
 
  // for documentation, see the Mapping base class
  virtual void
  transform(const ArrayView<const DerivativeForm<2, dim, spacedim>> &input,
            const MappingKind                                        kind,
            const typename Mapping<dim, spacedim>::InternalDataBase &internal,
            const ArrayView<Tensor<3, spacedim>> &output) const override;
 
  // for documentation, see the Mapping base class
  virtual void
  transform(const ArrayView<const Tensor<3, dim>> &                  input,
            const MappingKind                                        kind,
            const typename Mapping<dim, spacedim>::InternalDataBase &internal,
            const ArrayView<Tensor<3, spacedim>> &output) const override;
 
  void
  fill_mapping_data_for_generic_points(
    const typename Triangulation<dim, spacedim>::cell_iterator &cell,
    const ArrayView<const Point<dim>> &                         unit_points,
    const UpdateFlags                                           update_flags,
    ::internal::FEValuesImplementation::MappingRelatedData<dim, spacedim>
      &output_data) const;
 
  class InternalData : public Mapping<dim, spacedim>::InternalDataBase
  {
  public:
    InternalData(const unsigned int polynomial_degree);
 
    void
    initialize(const UpdateFlags      update_flags,
               const Quadrature<dim> &quadrature,
               const unsigned int     n_original_q_points);
 
    void
    initialize_face(const UpdateFlags      update_flags,
                    const Quadrature<dim> &quadrature,
                    const unsigned int     n_original_q_points);
 
    void
    compute_shape_function_values(const std::vector<Point<dim>> &unit_points);
 
    const double &
    shape(const unsigned int qpoint, const unsigned int shape_nr) const;
 
    double &
    shape(const unsigned int qpoint, const unsigned int shape_nr);
 
    const Tensor<1, dim> &
    derivative(const unsigned int qpoint, const unsigned int shape_nr) const;
 
    Tensor<1, dim> &
    derivative(const unsigned int qpoint, const unsigned int shape_nr);
 
    const Tensor<2, dim> &
    second_derivative(const unsigned int qpoint,
                      const unsigned int shape_nr) const;
 
    Tensor<2, dim> &
    second_derivative(const unsigned int qpoint, const unsigned int shape_nr);
 
    const Tensor<3, dim> &
    third_derivative(const unsigned int qpoint,
                     const unsigned int shape_nr) const;
 
    Tensor<3, dim> &
    third_derivative(const unsigned int qpoint, const unsigned int shape_nr);
 
    const Tensor<4, dim> &
    fourth_derivative(const unsigned int qpoint,
                      const unsigned int shape_nr) const;
 
    Tensor<4, dim> &
    fourth_derivative(const unsigned int qpoint, const unsigned int shape_nr);
 
    virtual std::size_t
    memory_consumption() const override;
 
    AlignedVector<double> shape_values;
 
    AlignedVector<Tensor<1, dim>> shape_derivatives;
 
    AlignedVector<Tensor<2, dim>> shape_second_derivatives;
 
    AlignedVector<Tensor<3, dim>> shape_third_derivatives;
 
    AlignedVector<Tensor<4, dim>> shape_fourth_derivatives;
 
    std::array<std::vector<Tensor<1, dim>>,
               GeometryInfo<dim>::faces_per_cell *(dim - 1)>
      unit_tangentials;
 
    const unsigned int polynomial_degree;
 
    const unsigned int n_shape_functions;
 
    /*
     * The default line support points. Is used in when the shape function
     * values are computed.
     *
     * The number of quadrature points depends on the degree of this
     * class, and it matches the number of degrees of freedom of an
     * FE_Q<1>(this->degree).
     */
    QGaussLobatto<1> line_support_points;
 
    using VectorizedArrayType =
      VectorizedArray<double,
                      std::min<std::size_t>(VectorizedArray<double>::size(),
                                            (dim <= 2 ? 2 : 4))>;
 
    internal::MatrixFreeFunctions::ShapeInfo<VectorizedArrayType> shape_info;
 
    mutable AlignedVector<VectorizedArrayType> scratch;
 
    bool tensor_product_quadrature;
 
    mutable AlignedVector<DerivativeForm<1, dim, spacedim>> covariant;
 
    mutable AlignedVector<DerivativeForm<1, dim, spacedim>> contravariant;
 
    mutable std::vector<AlignedVector<Tensor<1, spacedim>>> aux;
 
    mutable std::vector<Point<spacedim>> mapping_support_points;
 
    mutable typename Triangulation<dim, spacedim>::cell_iterator
      cell_of_current_support_points;
 
    mutable AlignedVector<double> volume_elements;
  };
 
protected:
  // documentation can be found in Mapping::requires_update_flags()
  virtual UpdateFlags
  requires_update_flags(const UpdateFlags update_flags) const override;
 
  // documentation can be found in Mapping::get_data()
  virtual std::unique_ptr<typename Mapping<dim, spacedim>::InternalDataBase>
  get_data(const UpdateFlags, const Quadrature<dim> &quadrature) const override;
 
  using Mapping<dim, spacedim>::get_face_data;
 
  // documentation can be found in Mapping::get_face_data()
  virtual std::unique_ptr<typename Mapping<dim, spacedim>::InternalDataBase>
  get_face_data(const UpdateFlags               flags,
                const hp::QCollection<dim - 1> &quadrature) const override;
 
  // documentation can be found in Mapping::get_subface_data()
  virtual std::unique_ptr<typename Mapping<dim, spacedim>::InternalDataBase>
  get_subface_data(const UpdateFlags          flags,
                   const Quadrature<dim - 1> &quadrature) const override;
 
  // documentation can be found in Mapping::fill_fe_values()
  virtual CellSimilarity::Similarity
  fill_fe_values(
    const typename Triangulation<dim, spacedim>::cell_iterator &cell,
    const CellSimilarity::Similarity                            cell_similarity,
    const Quadrature<dim> &                                     quadrature,
    const typename Mapping<dim, spacedim>::InternalDataBase &   internal_data,
    ::internal::FEValuesImplementation::MappingRelatedData<dim, spacedim>
      &output_data) const override;
 
  using Mapping<dim, spacedim>::fill_fe_face_values;
 
  // documentation can be found in Mapping::fill_fe_face_values()
  virtual void
  fill_fe_face_values(
    const typename Triangulation<dim, spacedim>::cell_iterator &cell,
    const unsigned int                                          face_no,
    const hp::QCollection<dim - 1> &                            quadrature,
    const typename Mapping<dim, spacedim>::InternalDataBase &   internal_data,
    ::internal::FEValuesImplementation::MappingRelatedData<dim, spacedim>
      &output_data) const override;
 
  // documentation can be found in Mapping::fill_fe_subface_values()
  virtual void
  fill_fe_subface_values(
    const typename Triangulation<dim, spacedim>::cell_iterator &cell,
    const unsigned int                                          face_no,
    const unsigned int                                          subface_no,
    const Quadrature<dim - 1> &                                 quadrature,
    const typename Mapping<dim, spacedim>::InternalDataBase &   internal_data,
    ::internal::FEValuesImplementation::MappingRelatedData<dim, spacedim>
      &output_data) const override;
 
  // documentation can be found in Mapping::fill_fe_immersed_surface_values()
  virtual void
  fill_fe_immersed_surface_values(
    const typename Triangulation<dim, spacedim>::cell_iterator &cell,
    const NonMatching::ImmersedSurfaceQuadrature<dim> &         quadrature,
    const typename Mapping<dim, spacedim>::InternalDataBase &   internal_data,
    ::internal::FEValuesImplementation::MappingRelatedData<dim, spacedim>
      &output_data) const override;
 
  const unsigned int polynomial_degree;
 
  /*
   * The default line support points. These are used when computing the
   * location in real space of the support points on lines and quads, which
   * are needed by the Manifold<dim,spacedim> class.
   *
   * The number of points depends on the degree of this class, and it matches
   * the number of degrees of freedom of an FE_Q<1>(this->degree).
   */
  const std::vector<Point<1>> line_support_points;
 
  /*
   * The one-dimensional polynomials defined as Lagrange polynomials from the
   * line support points. These are used for point evaluations and match the
   * polynomial space of an FE_Q<1>(this->degree).
   */
  const std::vector<Polynomials::Polynomial<double>> polynomials_1d;
 
  /*
   * The numbering from the lexicographic to the hierarchical ordering used
   * when expanding the tensor product with the mapping support points (which
   * come in hierarchical numbers).
   */
  const std::vector<unsigned int> renumber_lexicographic_to_hierarchic;
 
  /*
   * The support points in reference coordinates. These are used for
   * constructing approximations of the output of
   * compute_mapping_support_points() when evaluating the mapping on the fly,
   * rather than going through the FEValues interface provided by
   * InternalData.
   *
   * The number of points depends on the degree of this class, and it matches
   * the number of degrees of freedom of an FE_Q<dim>(this->degree).
   */
  const std::vector<Point<dim>> unit_cell_support_points;
 
  const std::vector<Table<2, double>>
    support_point_weights_perimeter_to_interior;
 
  const Table<2, double> support_point_weights_cell;
 
  virtual std::vector<Point<spacedim>>
  compute_mapping_support_points(
    const typename Triangulation<dim, spacedim>::cell_iterator &cell) const;
 
  Point<dim>
  transform_real_to_unit_cell_internal(
    const typename Triangulation<dim, spacedim>::cell_iterator &cell,
    const Point<spacedim> &                                     p,
    const Point<dim> &initial_p_unit) const;
 
  virtual void
  add_line_support_points(
    const typename Triangulation<dim, spacedim>::cell_iterator &cell,
    std::vector<Point<spacedim>> &                              a) const;
 
  virtual void
  add_quad_support_points(
    const typename Triangulation<dim, spacedim>::cell_iterator &cell,
    std::vector<Point<spacedim>> &                              a) const;
 
  // Make MappingQCache a friend since it needs to call the
  // compute_mapping_support_points() function.
  template <int, int>
  friend class MappingQCache;
};
 
 
 
template <int dim, int spacedim = dim>
using MappingQGeneric = MappingQ<dim, spacedim>;
 
/*----------------------------------------------------------------------*/
 
#ifndef DOXYGEN
 
template <int dim, int spacedim>
inline const double &
MappingQ<dim, spacedim>::InternalData::shape(const unsigned int qpoint,
                                             const unsigned int shape_nr) const
{
  AssertIndexRange(qpoint * n_shape_functions + shape_nr, shape_values.size());
  return shape_values[qpoint * n_shape_functions + shape_nr];
}
 
 
 
template <int dim, int spacedim>
inline double &
MappingQ<dim, spacedim>::InternalData::shape(const unsigned int qpoint,
                                             const unsigned int shape_nr)
{
  AssertIndexRange(qpoint * n_shape_functions + shape_nr, shape_values.size());
  return shape_values[qpoint * n_shape_functions + shape_nr];
}
 
 
template <int dim, int spacedim>
inline const Tensor<1, dim> &
MappingQ<dim, spacedim>::InternalData::derivative(
  const unsigned int qpoint,
  const unsigned int shape_nr) const
{
  AssertIndexRange(qpoint * n_shape_functions + shape_nr,
                   shape_derivatives.size());
  return shape_derivatives[qpoint * n_shape_functions + shape_nr];
}
 
 
 
template <int dim, int spacedim>
inline Tensor<1, dim> &
MappingQ<dim, spacedim>::InternalData::derivative(const unsigned int qpoint,
                                                  const unsigned int shape_nr)
{
  AssertIndexRange(qpoint * n_shape_functions + shape_nr,
                   shape_derivatives.size());
  return shape_derivatives[qpoint * n_shape_functions + shape_nr];
}
 
 
template <int dim, int spacedim>
inline const Tensor<2, dim> &
MappingQ<dim, spacedim>::InternalData::second_derivative(
  const unsigned int qpoint,
  const unsigned int shape_nr) const
{
  AssertIndexRange(qpoint * n_shape_functions + shape_nr,
                   shape_second_derivatives.size());
  return shape_second_derivatives[qpoint * n_shape_functions + shape_nr];
}
 
 
template <int dim, int spacedim>
inline Tensor<2, dim> &
MappingQ<dim, spacedim>::InternalData::second_derivative(
  const unsigned int qpoint,
  const unsigned int shape_nr)
{
  AssertIndexRange(qpoint * n_shape_functions + shape_nr,
                   shape_second_derivatives.size());
  return shape_second_derivatives[qpoint * n_shape_functions + shape_nr];
}
 
template <int dim, int spacedim>
inline const Tensor<3, dim> &
MappingQ<dim, spacedim>::InternalData::third_derivative(
  const unsigned int qpoint,
  const unsigned int shape_nr) const
{
  AssertIndexRange(qpoint * n_shape_functions + shape_nr,
                   shape_third_derivatives.size());
  return shape_third_derivatives[qpoint * n_shape_functions + shape_nr];
}
 
 
template <int dim, int spacedim>
inline Tensor<3, dim> &
MappingQ<dim, spacedim>::InternalData::third_derivative(
  const unsigned int qpoint,
  const unsigned int shape_nr)
{
  AssertIndexRange(qpoint * n_shape_functions + shape_nr,
                   shape_third_derivatives.size());
  return shape_third_derivatives[qpoint * n_shape_functions + shape_nr];
}
 
 
template <int dim, int spacedim>
inline const Tensor<4, dim> &
MappingQ<dim, spacedim>::InternalData::fourth_derivative(
  const unsigned int qpoint,
  const unsigned int shape_nr) const
{
  AssertIndexRange(qpoint * n_shape_functions + shape_nr,
                   shape_fourth_derivatives.size());
  return shape_fourth_derivatives[qpoint * n_shape_functions + shape_nr];
}
 
 
template <int dim, int spacedim>
inline Tensor<4, dim> &
MappingQ<dim, spacedim>::InternalData::fourth_derivative(
  const unsigned int qpoint,
  const unsigned int shape_nr)
{
  AssertIndexRange(qpoint * n_shape_functions + shape_nr,
                   shape_fourth_derivatives.size());
  return shape_fourth_derivatives[qpoint * n_shape_functions + shape_nr];
}
 
 
 
template <int dim, int spacedim>
inline bool
MappingQ<dim, spacedim>::preserves_vertex_locations() const
{
  return true;
}
 
#endif // DOXYGEN
 
/* -------------- declaration of explicit specializations ------------- */
 
 
DEAL_II_NAMESPACE_CLOSE
 
#endif