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 at
// the top level of the deal.II distribution.
//
// ---------------------------------------------------------------------

#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/lac/vector.h>
#include <deal.II/dofs/dof_handler.h>
#include <deal.II/fe/mapping.h>
#include <deal.II/fe/fe.h>
#include <deal.II/fe/fe_values.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