mapping_manifold.h

// ---------------------------------------------------------------------
//
// Copyright (C) 2016 - 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_manifold_h
#define dealii_mapping_manifold_h


#include <deal.II/base/config.h>
#include <deal.II/base/derivative_form.h>
#include <deal.II/base/table.h>
#include <deal.II/base/quadrature_lib.h>
#include <deal.II/base/qprojector.h>
#include <deal.II/grid/tria_iterator.h>
#include <deal.II/dofs/dof_accessor.h>
#include <deal.II/fe/mapping.h>

#include <cmath>

DEAL_II_NAMESPACE_OPEN

template <int,int> class MappingQ;




template <int dim, int spacedim=dim>
class MappingManifold : public Mapping<dim,spacedim>
{
public:
  MappingManifold () = default;

  MappingManifold (const MappingManifold<dim,spacedim> &mapping);

  // for documentation, see the Mapping base class
  virtual
  std::unique_ptr<Mapping<dim,spacedim>> clone () const override;

  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 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;

public:
  class InternalData : public Mapping<dim,spacedim>::InternalDataBase
  {
  public:
    InternalData() = default;

    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_manifold_quadrature_weights(const Quadrature<dim> &quadrature);

    void
    store_vertices(const typename Triangulation<dim,spacedim>::cell_iterator &cell) const;

    virtual
    std::size_t memory_consumption () const override;

    mutable std::vector<Point<spacedim> > vertices;

    mutable typename Triangulation<dim,spacedim>::cell_iterator cell;

    Quadrature<dim> quad;


    std::vector<std::vector<double> > cell_manifold_quadrature_weights;


    mutable std::vector<double> vertex_weights;

    std::array<std::vector<Tensor<1,dim> >, GeometryInfo<dim>::faces_per_cell *(dim-1)> unit_tangentials;

    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<double> volume_elements;

    mutable SmartPointer<const Manifold<dim,spacedim> > manifold;
  };


  // 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;

};



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

#ifndef DOXYGEN

template <int dim, int spacedim>
inline
void
MappingManifold<dim,spacedim>::InternalData::store_vertices (const typename Triangulation<dim,spacedim>::cell_iterator &cell) const
{
  vertices.resize(GeometryInfo<dim>::vertices_per_cell);
  for (unsigned int i=0; i<GeometryInfo<dim>::vertices_per_cell; ++i)
    vertices[i] = cell->vertex(i);
  this->cell = cell;
}


template <int dim, int spacedim>
inline
void
MappingManifold<dim,spacedim>::InternalData::compute_manifold_quadrature_weights (const Quadrature<dim> &quad)
{
  cell_manifold_quadrature_weights.resize(quad.size(), std::vector<double>(GeometryInfo<dim>::vertices_per_cell));
  for (unsigned int q=0; q<quad.size(); ++q)
    {
      for (unsigned int i=0; i<GeometryInfo<dim>::vertices_per_cell; ++i)
        {
          cell_manifold_quadrature_weights[q][i] = GeometryInfo<dim>::d_linear_shape_function(quad.point(q), i);
        }
    }
}



template <int dim, int spacedim>
inline
bool
MappingManifold<dim,spacedim>::preserves_vertex_locations () const
{
  return true;
}

#endif // DOXYGEN

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


DEAL_II_NAMESPACE_CLOSE

#endif