fe_poly_tensor.h

// ---------------------------------------------------------------------
//
// Copyright (C) 2005 - 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_tensor_h
#define dealii_fe_poly_tensor_h


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

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

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

#include <deal.II/lac/full_matrix.h>


DEAL_II_NAMESPACE_OPEN

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

  // 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;

  // documentation inherited from the base class
  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;

  // documentation inherited from the base class
  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;

  // documentation inherited from the base class
  virtual Tensor<2, dim>
  shape_grad_grad_component(const unsigned int i,
                            const Point<dim> & p,
                            const unsigned int component) const override;

protected:
  MappingType mapping_type;


  /* 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();

    // some scratch arrays
    std::vector<Tensor<1, dim>> values(0);
    std::vector<Tensor<2, dim>> grads(0);
    std::vector<Tensor<3, dim>> grad_grads(0);
    std::vector<Tensor<4, dim>> third_derivatives(0);
    std::vector<Tensor<5, dim>> fourth_derivatives(0);

    if (update_flags & (update_values | update_gradients | update_hessians))
      data.sign_change.resize(this->dofs_per_cell);

    // initialize fields only if really
    // necessary. otherwise, don't
    // allocate memory
    if (update_flags & update_values)
      {
        values.resize(this->dofs_per_cell);
        data.shape_values.reinit(this->dofs_per_cell, n_q_points);
        if (mapping_type != mapping_none)
          data.transformed_shape_values.resize(n_q_points);
      }

    if (update_flags & update_gradients)
      {
        grads.resize(this->dofs_per_cell);
        data.shape_grads.reinit(this->dofs_per_cell, n_q_points);
        data.transformed_shape_grads.resize(n_q_points);

        if ((mapping_type == mapping_raviart_thomas) ||
            (mapping_type == mapping_piola) ||
            (mapping_type == mapping_nedelec) ||
            (mapping_type == mapping_contravariant))
          data.untransformed_shape_grads.resize(n_q_points);
      }

    if (update_flags & update_hessians)
      {
        grad_grads.resize(this->dofs_per_cell);
        data.shape_grad_grads.reinit(this->dofs_per_cell, n_q_points);
        data.transformed_shape_hessians.resize(n_q_points);
        if (mapping_type != mapping_none)
          data.untransformed_shape_hessian_tensors.resize(n_q_points);
      }

    // Compute shape function values
    // and derivatives and hessians on
    // the reference cell.
    // Make sure, that for the
    // node values N_i holds
    // N_i(v_j)=\delta_ij for all basis
    // functions v_j
    if (update_flags & (update_values | update_gradients))
      for (unsigned int k = 0; k < n_q_points; ++k)
        {
          poly_space.compute(quadrature.point(k),
                             values,
                             grads,
                             grad_grads,
                             third_derivatives,
                             fourth_derivatives);

          if (update_flags & update_values)
            {
              if (inverse_node_matrix.n_cols() == 0)
                for (unsigned int i = 0; i < this->dofs_per_cell; ++i)
                  data.shape_values[i][k] = values[i];
              else
                for (unsigned int i = 0; i < this->dofs_per_cell; ++i)
                  {
                    Tensor<1, dim> add_values;
                    for (unsigned int j = 0; j < this->dofs_per_cell; ++j)
                      add_values += inverse_node_matrix(j, i) * values[j];
                    data.shape_values[i][k] = add_values;
                  }
            }

          if (update_flags & update_gradients)
            {
              if (inverse_node_matrix.n_cols() == 0)
                for (unsigned int i = 0; i < this->dofs_per_cell; ++i)
                  data.shape_grads[i][k] = grads[i];
              else
                for (unsigned int i = 0; i < this->dofs_per_cell; ++i)
                  {
                    Tensor<2, dim> add_grads;
                    for (unsigned int j = 0; j < this->dofs_per_cell; ++j)
                      add_grads += inverse_node_matrix(j, i) * grads[j];
                    data.shape_grads[i][k] = add_grads;
                  }
            }

          if (update_flags & update_hessians)
            {
              if (inverse_node_matrix.n_cols() == 0)
                for (unsigned int i = 0; i < this->dofs_per_cell; ++i)
                  data.shape_grad_grads[i][k] = grad_grads[i];
              else
                for (unsigned int i = 0; i < this->dofs_per_cell; ++i)
                  {
                    Tensor<3, dim> add_grad_grads;
                    for (unsigned int j = 0; j < this->dofs_per_cell; ++j)
                      add_grad_grads +=
                        inverse_node_matrix(j, i) * grad_grads[j];
                    data.shape_grad_grads[i][k] = add_grad_grads;
                  }
            }
        }
    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, Tensor<1, dim>> shape_values;

    Table<2, DerivativeForm<1, dim, spacedim>> shape_grads;

    Table<2, DerivativeForm<2, dim, spacedim>> shape_grad_grads;

    mutable std::vector<double>              sign_change;
    mutable std::vector<Tensor<1, spacedim>> transformed_shape_values;
    // for shape_gradient computations
    mutable std::vector<Tensor<2, spacedim>> transformed_shape_grads;
    mutable std::vector<Tensor<2, dim>>      untransformed_shape_grads;
    // for shape_hessian computations
    mutable std::vector<Tensor<3, spacedim>> transformed_shape_hessians;
    mutable std::vector<Tensor<3, dim>> untransformed_shape_hessian_tensors;
  };



  PolynomialType poly_space;

  FullMatrix<double> inverse_node_matrix;

  mutable Threads::Mutex cache_mutex;

  mutable Point<dim> cached_point;

  mutable std::vector<Tensor<1, dim>> cached_values;

  mutable std::vector<Tensor<2, dim>> cached_grads;

  mutable std::vector<Tensor<3, dim>> cached_grad_grads;
};

DEAL_II_NAMESPACE_CLOSE

#endif