polynomial_space.h

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// ------------------------------------------------------------------------
//
// SPDX-License-Identifier: LGPL-2.1-or-later
// Copyright (C) 2002 - 2024 by the deal.II authors
//
// This file is part of the deal.II library.
//
// Part of the source code is dual licensed under Apache-2.0 WITH
// LLVM-exception OR LGPL-2.1-or-later. Detailed license information
// governing the source code and code contributions can be found in
// LICENSE.md and CONTRIBUTING.md at the top level directory of deal.II.
//
// ------------------------------------------------------------------------
 
#ifndef dealii_polynomial_space_h
#define dealii_polynomial_space_h
 
 
#include <deal.II/base/config.h>
 
#include <deal.II/base/exceptions.h>
#include <deal.II/base/ndarray.h>
#include <deal.II/base/observer_pointer.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 <vector>
 
DEAL_II_NAMESPACE_OPEN
 
template <int dim>
class PolynomialSpace : public ScalarPolynomialsBase<dim>
{
public:
  static constexpr unsigned int dimension = dim;
 
  template <class Pol>
  PolynomialSpace(const std::vector<Pol> &pols);
 
  template <typename StreamType>
  void
  output_indices(StreamType &out) const;
 
  void
  set_numbering(const std::vector<unsigned int> &renumber);
 
  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;
 
  static unsigned int
  n_polynomials(const unsigned int n);
 
  std::string
  name() const override;
 
  virtual std::unique_ptr<ScalarPolynomialsBase<dim>>
  clone() const override;
 
protected:
  std::array<unsigned int, dim>
  compute_index(const unsigned int n) const;
 
private:
  const std::vector<Polynomials::Polynomial<double>> polynomials;
 
  std::vector<unsigned int> index_map;
 
  std::vector<unsigned int> index_map_inverse;
};
 
 
/* -------------- declaration of explicit specializations --- */
 
template <>
std::array<unsigned int, 1>
PolynomialSpace<1>::compute_index(const unsigned int n) const;
template <>
std::array<unsigned int, 2>
PolynomialSpace<2>::compute_index(const unsigned int n) const;
template <>
std::array<unsigned int, 3>
PolynomialSpace<3>::compute_index(const unsigned int n) const;
 
 
 
/* -------------- inline and template functions ------------- */
 
template <int dim>
template <class Pol>
PolynomialSpace<dim>::PolynomialSpace(const std::vector<Pol> &pols)
  : ScalarPolynomialsBase<dim>(pols.size(), n_polynomials(pols.size()))
  , polynomials(pols.begin(), pols.end())
  , index_map(n_polynomials(pols.size()))
  , index_map_inverse(n_polynomials(pols.size()))
{
  // 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>
inline std::string
PolynomialSpace<dim>::name() const
{
  return "PolynomialSpace";
}
 
 
template <int dim>
template <typename StreamType>
void
PolynomialSpace<dim>::output_indices(StreamType &out) const
{
  for (unsigned int i = 0; i < this->n(); ++i)
    {
      const std::array<unsigned int, dim> ix = compute_index(i);
      out << i << "\t";
      for (unsigned int d = 0; d < dim; ++d)
        out << ix[d] << ' ';
      out << std::endl;
    }
}
 
template <int dim>
template <int order>
Tensor<order, dim>
PolynomialSpace<dim>::compute_derivative(const unsigned int i,
                                         const Point<dim>  &p) const
{
  const std::array<unsigned int, dim> indices = compute_index(i);
 
  ndarray<double, dim, order + 1> v;
  {
    std::vector<double> tmp(order + 1);
    for (unsigned int d = 0; d < dim; ++d)
      {
        polynomials[indices[d]].value(p[d], tmp);
        for (unsigned int j = 0; j < order + 1; ++j)
          v[d][j] = tmp[j];
      }
  }
 
  if constexpr (order == 1)
    {
      Tensor<1, dim> derivative;
      for (unsigned int d = 0; d < dim; ++d)
        {
          derivative[d] = 1.;
          for (unsigned int x = 0; x < dim; ++x)
            {
              unsigned int x_order = 0;
              if (d == x)
                ++x_order;
 
              derivative[d] *= v[x][x_order];
            }
        }
 
      return derivative;
    }
  else if constexpr (order == 2)
    {
      Tensor<2, dim> derivative;
      for (unsigned int d1 = 0; d1 < dim; ++d1)
        for (unsigned int d2 = 0; d2 < dim; ++d2)
          {
            derivative[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[d1][d2] *= v[x][x_order];
              }
          }
 
      return derivative;
    }
  else if constexpr (order == 3)
    {
      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[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[d1][d2][d3] *= v[x][x_order];
                }
            }
 
      return derivative;
    }
  else if constexpr (order == 4)
    {
      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[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[d1][d2][d3][d4] *= v[x][x_order];
                  }
              }
 
      return derivative;
    }
  else
    {
      DEAL_II_NOT_IMPLEMENTED();
      return {};
    }
}
 
 
 
template <int dim>
inline Tensor<1, dim>
PolynomialSpace<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>
PolynomialSpace<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>
PolynomialSpace<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>
PolynomialSpace<dim>::compute_4th_derivative(const unsigned int i,
                                             const Point<dim>  &p) const
{
  return compute_derivative<4>(i, p);
}
 
DEAL_II_NAMESPACE_CLOSE
 
#endif