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.md at
// the top level directory of deal.II.
//
// ---------------------------------------------------------------------

#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/qprojector.h>
#include <deal.II/base/quadrature_lib.h>
#include <deal.II/base/table.h>

#include <deal.II/dofs/dof_accessor.h>

#include <deal.II/fe/mapping.h>

#include <deal.II/grid/tria_iterator.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