tensor_product_polynomials.h

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//
// Copyright (C) 2000 - 2022 by the deal.II authors
//
// This file is part of the deal.II library.
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// it, and/or modify it under the terms of the GNU Lesser General
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// 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
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#ifndef dealii_tensor_product_polynomials_h
#define dealii_tensor_product_polynomials_h
 
 
#include <deal.II/base/config.h>
 
#include <deal.II/base/exceptions.h>
#include <deal.II/base/ndarray.h>
#include <deal.II/base/point.h>
#include <deal.II/base/polynomial.h>
#include <deal.II/base/scalar_polynomials_base.h>
#include <deal.II/base/tensor.h>
#include <deal.II/base/utilities.h>
 
#include <vector>
 
DEAL_II_NAMESPACE_OPEN
 
// Forward declarations for friends
// TODO: We may be able to modify these classes so they aren't
// required to be friends
template <int dim>
class TensorProductPolynomialsBubbles;
template <int dim>
class TensorProductPolynomialsConst;
 
template <int dim, typename PolynomialType = Polynomials::Polynomial<double>>
class TensorProductPolynomials : public ScalarPolynomialsBase<dim>
{
public:
  static constexpr unsigned int dimension = dim;
 
  template <class Pol>
  TensorProductPolynomials(const std::vector<Pol> &pols);
 
  void
  output_indices(std::ostream &out) const;
 
  void
  set_numbering(const std::vector<unsigned int> &renumber);
 
  const std::vector<unsigned int> &
  get_numbering() const;
 
  const std::vector<unsigned int> &
  get_numbering_inverse() const;
 
  void
  evaluate(const Point<dim> &           unit_point,
           std::vector<double> &        values,
           std::vector<Tensor<1, dim>> &grads,
           std::vector<Tensor<2, dim>> &grad_grads,
           std::vector<Tensor<3, dim>> &third_derivatives,
           std::vector<Tensor<4, dim>> &fourth_derivatives) const override;
 
  double
  compute_value(const unsigned int i, const Point<dim> &p) const override;
 
  template <int order>
  Tensor<order, dim>
  compute_derivative(const unsigned int i, const Point<dim> &p) const;
 
  virtual Tensor<1, dim>
  compute_1st_derivative(const unsigned int i,
                         const Point<dim> & p) const override;
 
  virtual Tensor<2, dim>
  compute_2nd_derivative(const unsigned int i,
                         const Point<dim> & p) const override;
 
  virtual Tensor<3, dim>
  compute_3rd_derivative(const unsigned int i,
                         const Point<dim> & p) const override;
 
  virtual Tensor<4, dim>
  compute_4th_derivative(const unsigned int i,
                         const Point<dim> & p) const override;
 
  Tensor<1, dim>
  compute_grad(const unsigned int i, const Point<dim> &p) const override;
 
  Tensor<2, dim>
  compute_grad_grad(const unsigned int i, const Point<dim> &p) const override;
 
  std::string
  name() const override;
 
  virtual std::unique_ptr<ScalarPolynomialsBase<dim>>
  clone() const override;
 
  virtual std::size_t
  memory_consumption() const override;
 
  std::vector<PolynomialType>
  get_underlying_polynomials() const;
 
protected:
  std::vector<PolynomialType> polynomials;
 
  std::vector<unsigned int> index_map;
 
  std::vector<unsigned int> index_map_inverse;
 
  void
  compute_index(const unsigned int             i,
                std::array<unsigned int, dim> &indices) const;
 
  friend class TensorProductPolynomialsBubbles<dim>;
 
  friend class TensorProductPolynomialsConst<dim>;
};
 
 
 
template <int dim>
class AnisotropicPolynomials : public ScalarPolynomialsBase<dim>
{
public:
  AnisotropicPolynomials(
    const std::vector<std::vector<Polynomials::Polynomial<double>>>
      &base_polynomials);
 
  void
  evaluate(const Point<dim> &           unit_point,
           std::vector<double> &        values,
           std::vector<Tensor<1, dim>> &grads,
           std::vector<Tensor<2, dim>> &grad_grads,
           std::vector<Tensor<3, dim>> &third_derivatives,
           std::vector<Tensor<4, dim>> &fourth_derivatives) const override;
 
  double
  compute_value(const unsigned int i, const Point<dim> &p) const override;
 
  template <int order>
  Tensor<order, dim>
  compute_derivative(const unsigned int i, const Point<dim> &p) const;
 
  virtual Tensor<1, dim>
  compute_1st_derivative(const unsigned int i,
                         const Point<dim> & p) const override;
 
  virtual Tensor<2, dim>
  compute_2nd_derivative(const unsigned int i,
                         const Point<dim> & p) const override;
 
  virtual Tensor<3, dim>
  compute_3rd_derivative(const unsigned int i,
                         const Point<dim> & p) const override;
 
  virtual Tensor<4, dim>
  compute_4th_derivative(const unsigned int i,
                         const Point<dim> & p) const override;
 
  Tensor<1, dim>
  compute_grad(const unsigned int i, const Point<dim> &p) const override;
 
  Tensor<2, dim>
  compute_grad_grad(const unsigned int i, const Point<dim> &p) const override;
 
  std::string
  name() const override;
 
  virtual std::unique_ptr<ScalarPolynomialsBase<dim>>
  clone() const override;
 
private:
  const std::vector<std::vector<Polynomials::Polynomial<double>>> polynomials;
 
  void
  compute_index(const unsigned int             i,
                std::array<unsigned int, dim> &indices) const;
 
  static unsigned int
  get_n_tensor_pols(
    const std::vector<std::vector<Polynomials::Polynomial<double>>> &pols);
};
 
#ifndef DOXYGEN
 
 
/* ---------------- template and inline functions ---------- */
 
 
template <int dim, typename PolynomialType>
template <class Pol>
inline TensorProductPolynomials<dim, PolynomialType>::TensorProductPolynomials(
  const std::vector<Pol> &pols)
  : ScalarPolynomialsBase<dim>(1, Utilities::fixed_power<dim>(pols.size()))
  , polynomials(pols.begin(), pols.end())
  , index_map(this->n())
  , index_map_inverse(this->n())
{
  // per default set this index map to identity. This map can be changed by
  // the user through the set_numbering() function
  for (unsigned int i = 0; i < this->n(); ++i)
    {
      index_map[i]         = i;
      index_map_inverse[i] = i;
    }
}
 
 
template <int dim, typename PolynomialType>
inline const std::vector<unsigned int> &
TensorProductPolynomials<dim, PolynomialType>::get_numbering() const
{
  return index_map;
}
 
 
template <int dim, typename PolynomialType>
inline const std::vector<unsigned int> &
TensorProductPolynomials<dim, PolynomialType>::get_numbering_inverse() const
{
  return index_map_inverse;
}
 
 
template <int dim, typename PolynomialType>
inline std::string
TensorProductPolynomials<dim, PolynomialType>::name() const
{
  return "TensorProductPolynomials";
}
 
 
template <int dim, typename PolynomialType>
template <int order>
Tensor<order, dim>
TensorProductPolynomials<dim, PolynomialType>::compute_derivative(
  const unsigned int i,
  const Point<dim> & p) const
{
  std::array<unsigned int, dim> indices;
  compute_index(i, indices);
 
  ndarray<double, dim, 5> v;
  {
    std::vector<double> tmp(5);
    for (unsigned int d = 0; d < dim; ++d)
      {
        polynomials[indices[d]].value(p(d), tmp);
        v[d][0] = tmp[0];
        v[d][1] = tmp[1];
        v[d][2] = tmp[2];
        v[d][3] = tmp[3];
        v[d][4] = tmp[4];
      }
  }
 
  Tensor<order, dim> derivative;
  switch (order)
    {
      case 1:
        {
          Tensor<1, dim> &derivative_1 =
            *reinterpret_cast<Tensor<1, dim> *>(&derivative);
          for (unsigned int d = 0; d < dim; ++d)
            {
              derivative_1[d] = 1.;
              for (unsigned int x = 0; x < dim; ++x)
                {
                  unsigned int x_order = 0;
                  if (d == x)
                    ++x_order;
 
                  derivative_1[d] *= v[x][x_order];
                }
            }
 
          return derivative;
        }
      case 2:
        {
          Tensor<2, dim> &derivative_2 =
            *reinterpret_cast<Tensor<2, dim> *>(&derivative);
          for (unsigned int d1 = 0; d1 < dim; ++d1)
            for (unsigned int d2 = 0; d2 < dim; ++d2)
              {
                derivative_2[d1][d2] = 1.;
                for (unsigned int x = 0; x < dim; ++x)
                  {
                    unsigned int x_order = 0;
                    if (d1 == x)
                      ++x_order;
                    if (d2 == x)
                      ++x_order;
 
                    derivative_2[d1][d2] *= v[x][x_order];
                  }
              }
 
          return derivative;
        }
      case 3:
        {
          Tensor<3, dim> &derivative_3 =
            *reinterpret_cast<Tensor<3, dim> *>(&derivative);
          for (unsigned int d1 = 0; d1 < dim; ++d1)
            for (unsigned int d2 = 0; d2 < dim; ++d2)
              for (unsigned int d3 = 0; d3 < dim; ++d3)
                {
                  derivative_3[d1][d2][d3] = 1.;
                  for (unsigned int x = 0; x < dim; ++x)
                    {
                      unsigned int x_order = 0;
                      if (d1 == x)
                        ++x_order;
                      if (d2 == x)
                        ++x_order;
                      if (d3 == x)
                        ++x_order;
 
                      derivative_3[d1][d2][d3] *= v[x][x_order];
                    }
                }
 
          return derivative;
        }
      case 4:
        {
          Tensor<4, dim> &derivative_4 =
            *reinterpret_cast<Tensor<4, dim> *>(&derivative);
          for (unsigned int d1 = 0; d1 < dim; ++d1)
            for (unsigned int d2 = 0; d2 < dim; ++d2)
              for (unsigned int d3 = 0; d3 < dim; ++d3)
                for (unsigned int d4 = 0; d4 < dim; ++d4)
                  {
                    derivative_4[d1][d2][d3][d4] = 1.;
                    for (unsigned int x = 0; x < dim; ++x)
                      {
                        unsigned int x_order = 0;
                        if (d1 == x)
                          ++x_order;
                        if (d2 == x)
                          ++x_order;
                        if (d3 == x)
                          ++x_order;
                        if (d4 == x)
                          ++x_order;
 
                        derivative_4[d1][d2][d3][d4] *= v[x][x_order];
                      }
                  }
 
          return derivative;
        }
      default:
        {
          Assert(false, ExcNotImplemented());
          return derivative;
        }
    }
}
 
 
 
template <>
template <int order>
Tensor<order, 0>
TensorProductPolynomials<0, Polynomials::Polynomial<double>>::
  compute_derivative(const unsigned int, const Point<0> &) const
{
  AssertThrow(false, ExcNotImplemented());
 
  return {};
}
 
 
 
template <int dim, typename PolynomialType>
inline Tensor<1, dim>
TensorProductPolynomials<dim, PolynomialType>::compute_1st_derivative(
  const unsigned int i,
  const Point<dim> & p) const
{
  return compute_derivative<1>(i, p);
}
 
 
 
template <int dim, typename PolynomialType>
inline Tensor<2, dim>
TensorProductPolynomials<dim, PolynomialType>::compute_2nd_derivative(
  const unsigned int i,
  const Point<dim> & p) const
{
  return compute_derivative<2>(i, p);
}
 
 
 
template <int dim, typename PolynomialType>
inline Tensor<3, dim>
TensorProductPolynomials<dim, PolynomialType>::compute_3rd_derivative(
  const unsigned int i,
  const Point<dim> & p) const
{
  return compute_derivative<3>(i, p);
}
 
 
 
template <int dim, typename PolynomialType>
inline Tensor<4, dim>
TensorProductPolynomials<dim, PolynomialType>::compute_4th_derivative(
  const unsigned int i,
  const Point<dim> & p) const
{
  return compute_derivative<4>(i, p);
}
 
 
 
template <int dim>
template <int order>
Tensor<order, dim>
AnisotropicPolynomials<dim>::compute_derivative(const unsigned int i,
                                                const Point<dim> & p) const
{
  std::array<unsigned int, dim> indices;
  compute_index(i, indices);
 
  std::vector<std::vector<double>> v(dim, std::vector<double>(order + 1));
  for (unsigned int d = 0; d < dim; ++d)
    polynomials[d][indices[d]].value(p(d), v[d]);
 
  Tensor<order, dim> derivative;
  switch (order)
    {
      case 1:
        {
          Tensor<1, dim> &derivative_1 =
            *reinterpret_cast<Tensor<1, dim> *>(&derivative);
          for (unsigned int d = 0; d < dim; ++d)
            {
              derivative_1[d] = 1.;
              for (unsigned int x = 0; x < dim; ++x)
                {
                  unsigned int x_order = 0;
                  if (d == x)
                    ++x_order;
 
                  derivative_1[d] *= v[x][x_order];
                }
            }
 
          return derivative;
        }
      case 2:
        {
          Tensor<2, dim> &derivative_2 =
            *reinterpret_cast<Tensor<2, dim> *>(&derivative);
          for (unsigned int d1 = 0; d1 < dim; ++d1)
            for (unsigned int d2 = 0; d2 < dim; ++d2)
              {
                derivative_2[d1][d2] = 1.;
                for (unsigned int x = 0; x < dim; ++x)
                  {
                    unsigned int x_order = 0;
                    if (d1 == x)
                      ++x_order;
                    if (d2 == x)
                      ++x_order;
 
                    derivative_2[d1][d2] *= v[x][x_order];
                  }
              }
 
          return derivative;
        }
      case 3:
        {
          Tensor<3, dim> &derivative_3 =
            *reinterpret_cast<Tensor<3, dim> *>(&derivative);
          for (unsigned int d1 = 0; d1 < dim; ++d1)
            for (unsigned int d2 = 0; d2 < dim; ++d2)
              for (unsigned int d3 = 0; d3 < dim; ++d3)
                {
                  derivative_3[d1][d2][d3] = 1.;
                  for (unsigned int x = 0; x < dim; ++x)
                    {
                      unsigned int x_order = 0;
                      if (d1 == x)
                        ++x_order;
                      if (d2 == x)
                        ++x_order;
                      if (d3 == x)
                        ++x_order;
 
                      derivative_3[d1][d2][d3] *= v[x][x_order];
                    }
                }
 
          return derivative;
        }
      case 4:
        {
          Tensor<4, dim> &derivative_4 =
            *reinterpret_cast<Tensor<4, dim> *>(&derivative);
          for (unsigned int d1 = 0; d1 < dim; ++d1)
            for (unsigned int d2 = 0; d2 < dim; ++d2)
              for (unsigned int d3 = 0; d3 < dim; ++d3)
                for (unsigned int d4 = 0; d4 < dim; ++d4)
                  {
                    derivative_4[d1][d2][d3][d4] = 1.;
                    for (unsigned int x = 0; x < dim; ++x)
                      {
                        unsigned int x_order = 0;
                        if (d1 == x)
                          ++x_order;
                        if (d2 == x)
                          ++x_order;
                        if (d3 == x)
                          ++x_order;
                        if (d4 == x)
                          ++x_order;
 
                        derivative_4[d1][d2][d3][d4] *= v[x][x_order];
                      }
                  }
 
          return derivative;
        }
      default:
        {
          Assert(false, ExcNotImplemented());
          return derivative;
        }
    }
}
 
 
 
template <>
template <int order>
Tensor<order, 0>
AnisotropicPolynomials<0>::compute_derivative(const unsigned int,
                                              const Point<0> &) const
{
  AssertThrow(false, ExcNotImplemented());
 
  return {};
}
 
 
 
template <int dim>
inline Tensor<1, dim>
AnisotropicPolynomials<dim>::compute_1st_derivative(const unsigned int i,
                                                    const Point<dim> & p) const
{
  return compute_derivative<1>(i, p);
}
 
 
 
template <int dim>
inline Tensor<2, dim>
AnisotropicPolynomials<dim>::compute_2nd_derivative(const unsigned int i,
                                                    const Point<dim> & p) const
{
  return compute_derivative<2>(i, p);
}
 
 
 
template <int dim>
inline Tensor<3, dim>
AnisotropicPolynomials<dim>::compute_3rd_derivative(const unsigned int i,
                                                    const Point<dim> & p) const
{
  return compute_derivative<3>(i, p);
}
 
 
 
template <int dim>
inline Tensor<4, dim>
AnisotropicPolynomials<dim>::compute_4th_derivative(const unsigned int i,
                                                    const Point<dim> & p) const
{
  return compute_derivative<4>(i, p);
}
 
 
 
template <int dim>
inline std::string
AnisotropicPolynomials<dim>::name() const
{
  return "AnisotropicPolynomials";
}
 
 
 
#endif // DOXYGEN
DEAL_II_NAMESPACE_CLOSE
 
#endif