fe_poly.h

// ---------------------------------------------------------------------
//
// Copyright (C) 2004 - 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_poly_h
#define dealii_fe_poly_h


#include <deal.II/base/quadrature.h>
#include <deal.II/base/std_cxx14/memory.h>

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

DEAL_II_NAMESPACE_OPEN


template <class PolynomialType,
          int dim      = PolynomialType::dimension,
          int spacedim = dim>
class FE_Poly : public FiniteElement<dim, spacedim>
{
public:
  FE_Poly(const PolynomialType &            poly_space,
          const FiniteElementData<dim> &    fe_data,
          const std::vector<bool> &         restriction_is_additive_flags,
          const std::vector<ComponentMask> &nonzero_components);

  unsigned int
  get_degree() const;

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

  std::vector<unsigned int>
  get_poly_space_numbering() const;

  std::vector<unsigned int>
  get_poly_space_numbering_inverse() const;

  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;

  virtual Tensor<3, dim>
  shape_3rd_derivative(const unsigned int i,
                       const Point<dim> & p) const override;

  virtual Tensor<3, dim>
  shape_3rd_derivative_component(const unsigned int i,
                                 const Point<dim> & p,
                                 const unsigned int component) const override;

  virtual Tensor<4, dim>
  shape_4th_derivative(const unsigned int i,
                       const Point<dim> & p) const override;

  virtual Tensor<4, dim>
  shape_4th_derivative_component(const unsigned int i,
                                 const Point<dim> & p,
                                 const unsigned int component) const override;

protected:
  /*
   * NOTE: The following function has its definition inlined into the class
   * declaration because we otherwise run into a compiler error with MS Visual
   * Studio.
   */


  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
  {
    // generate a new data object and
    // initialize some fields
    std::unique_ptr<typename FiniteElement<dim, spacedim>::InternalDataBase>
          data_ptr   = std_cxx14::make_unique<InternalData>();
    auto &data       = dynamic_cast<InternalData &>(*data_ptr);
    data.update_each = requires_update_flags(update_flags);

    const unsigned int n_q_points = quadrature.size();

    // initialize some scratch arrays. we need them for the underlying
    // polynomial to put the values and derivatives of shape functions
    // to put there, depending on what the user requested
    std::vector<double> values(
      update_flags & update_values ? this->dofs_per_cell : 0);
    std::vector<Tensor<1, dim>> grads(
      update_flags & update_gradients ? this->dofs_per_cell : 0);
    std::vector<Tensor<2, dim>> grad_grads(
      update_flags & update_hessians ? this->dofs_per_cell : 0);
    std::vector<Tensor<3, dim>> third_derivatives(
      update_flags & update_3rd_derivatives ? this->dofs_per_cell : 0);
    std::vector<Tensor<4, dim>>
      fourth_derivatives; // won't be needed, so leave empty

    // now also initialize fields the fields of this class's own
    // temporary storage, depending on what we need for the given
    // update flags.
    //
    // there is one exception from the rule: if we are dealing with
    // cells (i.e., if this function is not called via
    // get_(sub)face_data()), then we can already store things in the
    // final location where FEValues::reinit() later wants to see
    // things. we then don't need the intermediate space. we determine
    // whether we are on a cell by asking whether the number of
    // elements in the output array equals the number of quadrature
    // points (yes, it's a cell) or not (because in that case the
    // number of quadrature points we use here equals the number of
    // quadrature points summed over *all* faces or subfaces, whereas
    // the number of output slots equals the number of quadrature
    // points on only *one* face)
    if ((update_flags & update_values) &&
        !((output_data.shape_values.n_rows() > 0) &&
          (output_data.shape_values.n_cols() == n_q_points)))
      data.shape_values.reinit(this->dofs_per_cell, n_q_points);

    if (update_flags & update_gradients)
      data.shape_gradients.reinit(this->dofs_per_cell, n_q_points);

    if (update_flags & update_hessians)
      data.shape_hessians.reinit(this->dofs_per_cell, n_q_points);

    if (update_flags & update_3rd_derivatives)
      data.shape_3rd_derivatives.reinit(this->dofs_per_cell, n_q_points);

    // next already fill those fields of which we have information by
    // now. note that the shape gradients are only those on the unit
    // cell, and need to be transformed when visiting an actual cell
    if (update_flags & (update_values | update_gradients | update_hessians |
                        update_3rd_derivatives))
      for (unsigned int i = 0; i < n_q_points; ++i)
        {
          poly_space.compute(quadrature.point(i),
                             values,
                             grads,
                             grad_grads,
                             third_derivatives,
                             fourth_derivatives);

          // the values of shape functions at quadrature points don't change.
          // consequently, write these values right into the output array if
          // we can, i.e., if the output array has the correct size. this is
          // the case on cells. on faces, we already precompute data on *all*
          // faces and subfaces, but we later on copy only a portion of it
          // into the output object; in that case, copy the data from all
          // faces into the scratch object
          if (update_flags & update_values)
            if (output_data.shape_values.n_rows() > 0)
              {
                if (output_data.shape_values.n_cols() == n_q_points)
                  for (unsigned int k = 0; k < this->dofs_per_cell; ++k)
                    output_data.shape_values[k][i] = values[k];
                else
                  for (unsigned int k = 0; k < this->dofs_per_cell; ++k)
                    data.shape_values[k][i] = values[k];
              }

          // for everything else, derivatives need to be transformed,
          // so we write them into our scratch space and only later
          // copy stuff into where FEValues wants it
          if (update_flags & update_gradients)
            for (unsigned int k = 0; k < this->dofs_per_cell; ++k)
              data.shape_gradients[k][i] = grads[k];

          if (update_flags & update_hessians)
            for (unsigned int k = 0; k < this->dofs_per_cell; ++k)
              data.shape_hessians[k][i] = grad_grads[k];

          if (update_flags & update_3rd_derivatives)
            for (unsigned int k = 0; k < this->dofs_per_cell; ++k)
              data.shape_3rd_derivatives[k][i] = third_derivatives[k];
        }
    return data_ptr;
  }

  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;

  class InternalData : public FiniteElement<dim, spacedim>::InternalDataBase
  {
  public:
    Table<2, double> shape_values;

    Table<2, Tensor<1, dim>> shape_gradients;

    Table<2, Tensor<2, dim>> shape_hessians;

    Table<2, Tensor<3, dim>> shape_3rd_derivatives;
  };

  void
  correct_third_derivatives(
    internal::FEValuesImplementation::FiniteElementRelatedData<dim, spacedim>
      &output_data,
    const internal::FEValuesImplementation::MappingRelatedData<dim, spacedim>
      &                mapping_data,
    const unsigned int n_q_points,
    const unsigned int dof) const;

  PolynomialType poly_space;
};

DEAL_II_NAMESPACE_CLOSE

#endif