mapping_q_generic.h

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//
// Copyright (C) 2000 - 2020 by the deal.II authors
//
// This file is part of the deal.II library.
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// it, and/or modify it under the terms of the GNU Lesser General
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#ifndef dealii_mapping_q_generic_h
#define dealii_mapping_q_generic_h


#include <deal.II/base/config.h>

#include <deal.II/base/derivative_form.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 <array>
#include <cmath>

DEAL_II_NAMESPACE_OPEN

template <int, int>
class MappingQ;

template <int, int>
class MappingQCache;




template <int dim, int spacedim = dim>
class MappingQGeneric : public Mapping<dim, spacedim>
{
public:
  MappingQGeneric(const unsigned int polynomial_degree);

  MappingQGeneric(const MappingQGeneric<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 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(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;

public:
  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;

    std::vector<double> shape_values;

    std::vector<Tensor<1, dim>> shape_derivatives;

    std::vector<Tensor<2, dim>> shape_second_derivatives;

    std::vector<Tensor<3, dim>> shape_third_derivatives;

    std::vector<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;

    internal::MatrixFreeFunctions::ShapeInfo<VectorizedArray<double>>
      shape_info;

    mutable AlignedVector<VectorizedArray<double>> scratch;

    mutable AlignedVector<VectorizedArray<double>> values_dofs;

    mutable AlignedVector<VectorizedArray<double>> values_quad;

    mutable AlignedVector<VectorizedArray<double>> gradients_quad;

    mutable AlignedVector<VectorizedArray<double>> hessians_quad;

    bool tensor_product_quadrature;

    mutable std::vector<DerivativeForm<1, dim, spacedim>> covariant;

    mutable std::vector<DerivativeForm<1, dim, spacedim>> contravariant;

    mutable std::vector<std::vector<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 std::vector<double> volume_elements;
  };


  // 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;

  // 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 Quadrature<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;

  // 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 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_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;

protected:
  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 asked to the Manifold<dim,spacedim> class.
   *
   * 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;

  std::vector<Table<2, double>> support_point_weights_perimeter_to_interior;

  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 MappingQ a friend since it needs to call the fill_fe_values()
  // functions on its MappingQGeneric(1) sub-object.
  template <int, int>
  friend class MappingQ;

  // Make MappingQCache a friend since it needs to call the
  // compute_mapping_support_points() function.
  template <int, int>
  friend class MappingQCache;
};



/*----------------------------------------------------------------------*/

#ifndef DOXYGEN

template <int dim, int spacedim>
inline const double &
MappingQGeneric<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 &
MappingQGeneric<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> &
MappingQGeneric<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> &
MappingQGeneric<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> &
MappingQGeneric<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> &
MappingQGeneric<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> &
MappingQGeneric<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> &
MappingQGeneric<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> &
MappingQGeneric<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> &
MappingQGeneric<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
MappingQGeneric<dim, spacedim>::preserves_vertex_locations() const
{
  return true;
}

#endif // DOXYGEN

/* -------------- declaration of explicit specializations ------------- */


DEAL_II_NAMESPACE_CLOSE

#endif