mapping_fe_field.h

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// -----------------------------------------------------------------------------
//
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception OR LGPL-2.1-or-later
// Copyright (C) 2015 - 2026 by the deal.II authors
//
// This file is part of the deal.II library.
//
// Detailed license information governing the source code and contributions
// can be found in LICENSE.md and CONTRIBUTING.md at the top level directory.
//
// -----------------------------------------------------------------------------
 
#ifndef dealii_mapping_fe_field_h
#define dealii_mapping_fe_field_h
 
 
#include <deal.II/base/config.h>
 
#include <deal.II/base/mg_level_object.h>
#include <deal.II/base/mutex.h>
 
#include <deal.II/dofs/dof_handler.h>
 
#include <deal.II/fe/fe.h>
#include <deal.II/fe/fe_values.h>
#include <deal.II/fe/mapping.h>
 
#include <deal.II/lac/vector.h>
 
#include <boost/container/small_vector.hpp>
 
#include <array>
 
 
DEAL_II_NAMESPACE_OPEN
 
namespace internal
{
  template <int dim, int spacedim = dim>
  class ComponentDoFs
  {
  public:
    ComponentDoFs(const FiniteElement<dim, spacedim> &fe,
                  const ComponentMask                &mask);
 
    bool
    all_components_are_primitive() const;
 
    ArrayView<const unsigned int>
    operator[](const unsigned int component) const;
 
  private:
    bool all_components_primitive;
 
    std::array<unsigned int, spacedim + 1> offsets;
 
    std::vector<unsigned int> component_dofs;
  };
} // namespace internal
 
template <int dim, int spacedim = dim, typename VectorType = Vector<double>>
class MappingFEField : public Mapping<dim, spacedim>
{
public:
  MappingFEField(const DoFHandler<dim, spacedim> &euler_dof_handler,
                 const VectorType                &euler_vector,
                 const ComponentMask             &mask = {});
 
  MappingFEField(const DoFHandler<dim, spacedim> &euler_dof_handler,
                 const std::vector<VectorType>   &euler_vector,
                 const ComponentMask             &mask = {});
 
  MappingFEField(const DoFHandler<dim, spacedim> &euler_dof_handler,
                 const MGLevelObject<VectorType> &euler_vector,
                 const ComponentMask             &mask = {});
 
  MappingFEField(const MappingFEField<dim, spacedim, VectorType> &mapping);
 
  virtual std::unique_ptr<Mapping<dim, spacedim>>
  clone() const override;
 
  virtual bool
  preserves_vertex_locations() const override;
 
  virtual bool
  is_compatible_with(const ReferenceCell<dim> &reference_cell) const override;
 
  virtual boost::container::small_vector<Point<spacedim>,
#ifndef _MSC_VER
                                         ReferenceCells::max_n_vertices<dim>()
#else
                                         GeometryInfo<dim>::vertices_per_cell
#endif
                                         >
  get_vertices(const typename Triangulation<dim, spacedim>::cell_iterator &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(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;
 
  unsigned int
  get_degree() const;
 
  ComponentMask
  get_component_mask() const;
 
  DeclException0(ExcInactiveCell);
 
private:
  // documentation can be found in Mapping::requires_update_flags()
  virtual UpdateFlags
  requires_update_flags(const UpdateFlags update_flags) const override;
 
public:
  class InternalData : public Mapping<dim, spacedim>::InternalDataBase
  {
  public:
    InternalData(const FiniteElement<dim, spacedim> &fe,
                 const ComponentMask                &mask);
 
    // Documentation see Mapping::InternalDataBase.
    virtual void
    reinit(const UpdateFlags      update_flags,
           const Quadrature<dim> &quadrature) override;
 
    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;
 
    ObserverPointer<const FiniteElement<dim, spacedim>> fe;
 
    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;
 
    unsigned int n_shape_functions;
 
    ComponentMask mask;
 
    mutable std::vector<DerivativeForm<1, dim, spacedim>> covariant;
 
    mutable std::vector<DerivativeForm<1, dim, spacedim>> contravariant;
 
    mutable std::vector<double> volume_elements;
 
    mutable std::vector<double> quadrature_weights;
 
    mutable std::vector<std::vector<Tensor<1, spacedim>>> aux;
 
    mutable std::vector<types::global_dof_index> local_dof_indices;
 
    mutable std::vector<double> local_dof_values;
  };
 
protected:
  // 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;
 
  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;
 
  ReferenceCell<dim> reference_cell;
 
  const bool uses_level_dofs;
 
  std::vector<ObserverPointer<const VectorType,
                              MappingFEField<dim, spacedim, VectorType>>>
    euler_vector;
 
  ObserverPointer<const DoFHandler<dim, spacedim>,
                  MappingFEField<dim, spacedim, VectorType>>
    euler_dof_handler;
 
private:
  Point<spacedim>
  do_transform_unit_to_real_cell(const InternalData &mdata) const;
 
  Point<dim>
  do_transform_real_to_unit_cell(
    const typename Triangulation<dim, spacedim>::cell_iterator &cell,
    const Point<spacedim>                                      &p,
    const Point<dim>                                           &starting_guess,
    InternalData                                               &mdata) const;
 
  void
  update_internal_dofs(
    const typename Triangulation<dim, spacedim>::cell_iterator &cell,
    const typename MappingFEField<dim, spacedim, VectorType>::InternalData
      &data) const;
 
  /*
   * Which components to use for the mapping.
   */
  const ComponentMask fe_mask;
 
  internal::ComponentDoFs<dim, spacedim> component_dofs;
 
  mutable FEValues<dim, spacedim> fe_values;
 
  mutable std::vector<types::global_dof_index> dof_indices;
 
  mutable Threads::Mutex fe_values_mutex;
 
  void
  compute_face_data(const unsigned int n_original_q_points,
                    InternalData      &data) const;
 
  // Declare other MappingFEField classes friends.
  template <int, int, class>
  friend class MappingFEField;
};
 
/* -------------- declaration of explicit specializations ------------- */
 
#ifndef DOXYGEN
 
#endif // DOXYGEN
 
DEAL_II_NAMESPACE_CLOSE
 
#endif