fe_nedelec_sz.h

// ---------------------------------------------------------------------
//
// Copyright (C) 2015 - 2019 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_nedelec_sz_h
#define dealii_fe_nedelec_sz_h

#include <deal.II/base/derivative_form.h>
#include <deal.II/base/polynomials_integrated_legendre_sz.h>
#include <deal.II/base/qprojector.h>

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

DEAL_II_NAMESPACE_OPEN


template <int dim, int spacedim = dim>
class FE_NedelecSZ : public FiniteElement<dim, dim>
{
public:
  static_assert(dim == spacedim,
                "FE_NedelecSZ is only implemented for dim==spacedim!");

  FE_NedelecSZ(const unsigned int degree);

  virtual UpdateFlags
  requires_update_flags(const UpdateFlags update_flags) const override;

  virtual std::string
  get_name() const override;

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

  UpdateFlags
  update_once(const UpdateFlags flags) const;

  UpdateFlags
  update_each(const UpdateFlags flags) const;

protected:
  MappingType mapping_type;

  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, dim>::cell_iterator &cell,
    const CellSimilarity::Similarity                       cell_similarity,
    const Quadrature<dim> &                                quadrature,
    const Mapping<dim, dim> &                              mapping,
    const typename Mapping<dim, dim>::InternalDataBase &   mapping_internal,
    const ::internal::FEValuesImplementation::MappingRelatedData<dim, dim>
      &                                                       mapping_data,
    const typename FiniteElement<dim, dim>::InternalDataBase &fedata,
    ::internal::FEValuesImplementation::FiniteElementRelatedData<dim, dim>
      &data) const override;

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

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

  class InternalData : public FiniteElement<dim, dim>::InternalDataBase
  {
  public:
    mutable std::vector<std::vector<Tensor<1, dim>>> shape_values;

    mutable std::vector<std::vector<DerivativeForm<1, dim, dim>>> shape_grads;

    std::vector<std::vector<std::vector<double>>> sigma_imj_values;

    std::vector<std::vector<std::vector<double>>> sigma_imj_grads;

    std::vector<std::vector<double>> edge_sigma_values;

    std::vector<std::vector<double>> edge_sigma_grads;

    std::vector<std::vector<double>> edge_lambda_values;

    std::vector<std::vector<double>> edge_lambda_grads_2d;

    std::vector<std::vector<std::vector<double>>> edge_lambda_grads_3d;

    std::vector<std::vector<std::vector<double>>> edge_lambda_gradgrads_3d;

    std::vector<std::vector<double>> face_lambda_values;

    std::vector<std::vector<double>> face_lambda_grads;
  };

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

  std::vector<Polynomials::Polynomial<double>> IntegratedLegendrePolynomials;

  void
  create_polynomials(const unsigned int degree);

  unsigned int
  compute_num_dofs(const unsigned int degree) const;

  void
  fill_edge_values(const typename Triangulation<dim, dim>::cell_iterator &cell,
                   const Quadrature<dim> &quadrature,
                   const InternalData &   fedata) const;

  void
  fill_face_values(const typename Triangulation<dim, dim>::cell_iterator &cell,
                   const Quadrature<dim> &quadrature,
                   const InternalData &   fedata) const;
};



DEAL_II_NAMESPACE_CLOSE

#endif