mapping_fe_field.h

// ---------------------------------------------------------------------
//
// Copyright (C) 2001 - 2018 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_fe_h
#define dealii_mapping_fe_h


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

#include <deal.II/base/table.h>
#include <deal.II/base/thread_management.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 <array>


DEAL_II_NAMESPACE_OPEN



template <int dim,
          int spacedim            = dim,
          typename VectorType     = Vector<double>,
          typename DoFHandlerType = DoFHandler<dim, spacedim>>
class MappingFEField : public Mapping<dim, spacedim>
{
public:
  MappingFEField(const DoFHandlerType &euler_dof_handler,
                 const VectorType &    euler_vector,
                 const ComponentMask & mask = ComponentMask());

  MappingFEField(
    const MappingFEField<dim, spacedim, VectorType, DoFHandlerType> &mapping);

  virtual std::unique_ptr<Mapping<dim, spacedim>>
  clone() const override;

  virtual bool
  preserves_vertex_locations() const override;

  virtual std::array<Point<spacedim>, GeometryInfo<dim>::vertices_per_cell>
  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 MappingType                                        type,
            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 MappingType                                        type,
            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 MappingType                                        type,
            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 MappingType                                        type,
            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 MappingType                                        type,
            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);

    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;

    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<std::vector<Tensor<1, spacedim>>> aux;

    mutable std::vector<types::global_dof_index> local_dof_indices;

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

private:
  // 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;

  SmartPointer<const VectorType,
               MappingFEField<dim, spacedim, VectorType, DoFHandlerType>>
    euler_vector;

  SmartPointer<const DoFHandlerType,
               MappingFEField<dim, spacedim, VectorType, DoFHandlerType>>
    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> &                                          initial_p_unit,
    InternalData &                                              mdata) const;

  void
  update_internal_dofs(
    const typename Triangulation<dim, spacedim>::cell_iterator &cell,
    const typename MappingFEField<dim, spacedim, VectorType, DoFHandlerType>::
      InternalData &data) const;

  virtual void
  compute_shapes_virtual(
    const std::vector<Point<dim>> &unit_points,
    typename MappingFEField<dim, spacedim, VectorType, DoFHandlerType>::
      InternalData &data) const;

  /*
   * Which components to use for the mapping.
   */
  const ComponentMask fe_mask;

  std::vector<unsigned int> fe_to_real;

  mutable FEValues<dim, spacedim> fe_values;

  mutable Threads::Mutex fe_values_mutex;

  void
  compute_data(const UpdateFlags      update_flags,
               const Quadrature<dim> &q,
               const unsigned int     n_original_q_points,
               InternalData &         data) const;

  void
  compute_face_data(const UpdateFlags      update_flags,
                    const Quadrature<dim> &q,
                    const unsigned int     n_original_q_points,
                    InternalData &         data) const;


  template <int, int, class, class>
  friend class MappingFEField;
};

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

#ifndef DOXYGEN

#endif // DOXYGEN

DEAL_II_NAMESPACE_CLOSE

#endif