fe_dgp_nonparametric.h

// ---------------------------------------------------------------------
//
// Copyright (C) 2002 - 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_fe_dgp_nonparametric_h
#define dealii_fe_dgp_nonparametric_h

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

#include <deal.II/base/polynomial.h>
#include <deal.II/base/polynomial_space.h>

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

DEAL_II_NAMESPACE_OPEN


template <int dim, int spacedim = dim>
class FE_DGPNonparametric : public FiniteElement<dim, spacedim>
{
public:
  FE_DGPNonparametric(const unsigned int k);

  virtual std::string
  get_name() const override;

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

  // for documentation, see the FiniteElement base class
  virtual UpdateFlags
  requires_update_flags(const UpdateFlags update_flags) const override;

  virtual double
  shape_value(const unsigned int i, const Point<dim> &p) const override;

  virtual double
  shape_value_component(const unsigned int i,
                        const Point<dim> & p,
                        const unsigned int component) const override;

  virtual Tensor<1, dim>
  shape_grad(const unsigned int i, const Point<dim> &p) const override;

  virtual Tensor<1, dim>
  shape_grad_component(const unsigned int i,
                       const Point<dim> & p,
                       const unsigned int component) const override;

  virtual Tensor<2, dim>
  shape_grad_grad(const unsigned int i, const Point<dim> &p) const override;

  virtual Tensor<2, dim>
  shape_grad_grad_component(const unsigned int i,
                            const Point<dim> & p,
                            const unsigned int component) const override;

  unsigned int
  get_degree() const;

  virtual void
  get_face_interpolation_matrix(const FiniteElement<dim, spacedim> &source,
                                FullMatrix<double> &matrix) const override;

  virtual void
  get_subface_interpolation_matrix(const FiniteElement<dim, spacedim> &source,
                                   const unsigned int                  subface,
                                   FullMatrix<double> &matrix) const override;

  virtual std::vector<std::pair<unsigned int, unsigned int>>
  hp_vertex_dof_identities(
    const FiniteElement<dim, spacedim> &fe_other) const override;

  virtual std::vector<std::pair<unsigned int, unsigned int>>
  hp_line_dof_identities(
    const FiniteElement<dim, spacedim> &fe_other) const override;

  virtual std::vector<std::pair<unsigned int, unsigned int>>
  hp_quad_dof_identities(
    const FiniteElement<dim, spacedim> &fe_other) const override;

  virtual bool
  hp_constraints_are_implemented() const override;

  virtual FiniteElementDomination::Domination
  compare_for_domination(const FiniteElement<dim, spacedim> &fe_other,
                         const unsigned int codim = 0) const override final;

  virtual bool
  has_support_on_face(const unsigned int shape_index,
                      const unsigned int face_index) const override;

  virtual std::size_t
  memory_consumption() const override;

protected:
  virtual std::unique_ptr<
    typename FiniteElement<dim, spacedim>::InternalDataBase>
  get_data(
    const UpdateFlags             update_flags,
    const Mapping<dim, spacedim> &mapping,
    const Quadrature<dim> &       quadrature,
    ::internal::FEValuesImplementation::FiniteElementRelatedData<dim,
                                                                       spacedim>
      &output_data) const override;

  virtual void
  fill_fe_values(
    const typename Triangulation<dim, spacedim>::cell_iterator &cell,
    const CellSimilarity::Similarity                            cell_similarity,
    const Quadrature<dim> &                                     quadrature,
    const Mapping<dim, spacedim> &                              mapping,
    const typename Mapping<dim, spacedim>::InternalDataBase &mapping_internal,
    const ::internal::FEValuesImplementation::MappingRelatedData<dim,
                                                                       spacedim>
      &                                                            mapping_data,
    const typename FiniteElement<dim, spacedim>::InternalDataBase &fe_internal,
    ::internal::FEValuesImplementation::FiniteElementRelatedData<dim,
                                                                       spacedim>
      &output_data) const override;

  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 Mapping<dim, spacedim> &                              mapping,
    const typename Mapping<dim, spacedim>::InternalDataBase &mapping_internal,
    const ::internal::FEValuesImplementation::MappingRelatedData<dim,
                                                                       spacedim>
      &                                                            mapping_data,
    const typename FiniteElement<dim, spacedim>::InternalDataBase &fe_internal,
    ::internal::FEValuesImplementation::FiniteElementRelatedData<dim,
                                                                       spacedim>
      &output_data) const override;

  virtual void
  fill_fe_subface_values(
    const typename Triangulation<dim, spacedim>::cell_iterator &cell,
    const unsigned int                                          face_no,
    const unsigned int                                          sub_no,
    const Quadrature<dim - 1> &                                 quadrature,
    const Mapping<dim, spacedim> &                              mapping,
    const typename Mapping<dim, spacedim>::InternalDataBase &mapping_internal,
    const ::internal::FEValuesImplementation::MappingRelatedData<dim,
                                                                       spacedim>
      &                                                            mapping_data,
    const typename FiniteElement<dim, spacedim>::InternalDataBase &fe_internal,
    ::internal::FEValuesImplementation::FiniteElementRelatedData<dim,
                                                                       spacedim>
      &output_data) const override;

private:
  static std::vector<unsigned int>
  get_dpo_vector(const unsigned int degree);

  const PolynomialSpace<dim> polynomial_space;

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

DEAL_II_NAMESPACE_CLOSE

#endif