polynomials_rannacher_turek.h

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// -----------------------------------------------------------------------------
//
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception OR LGPL-2.1-or-later
// Copyright (C) 2015 - 2025 by the deal.II authors
//
// This file is part of the deal.II library.
//
// Detailed license information governing the source code and contributions
// can be found in LICENSE.md and CONTRIBUTING.md at the top level directory.
//
// -----------------------------------------------------------------------------
 
 
#ifndef dealii_polynomials_rannacher_turek_h
#define dealii_polynomials_rannacher_turek_h
 
#include <deal.II/base/config.h>
 
#include <deal.II/base/exceptions.h>
#include <deal.II/base/point.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 PolynomialsRannacherTurek : public ScalarPolynomialsBase<dim>
{
public:
  static constexpr unsigned int dimension = dim;
 
  PolynomialsRannacherTurek();
 
  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;
 
  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;
 
  std::string
  name() const override;
 
  virtual std::unique_ptr<ScalarPolynomialsBase<dim>>
  clone() const override;
};
 
 
namespace internal
{
  namespace PolynomialsRannacherTurekImplementation
  {
    template <int order, int dim>
    inline Tensor<order, dim>
    compute_derivative(const unsigned int, const Point<dim> &)
    {
      Assert(dim == 2, ExcNotImplemented());
      return Tensor<order, dim>();
    }
 
 
    template <int order>
    inline Tensor<order, 2>
    compute_derivative(const unsigned int i, const Point<2> &p)
    {
      const unsigned int dim = 2;
 
      if constexpr (order == 1)
        {
          Tensor<1, dim> derivative;
          if (i == 0)
            {
              derivative[0] = -2.5 + 3 * p[0];
              derivative[1] = 1.5 - 3 * p[1];
            }
          else if (i == 1)
            {
              derivative[0] = -0.5 + 3.0 * p[0];
              derivative[1] = 1.5 - 3.0 * p[1];
            }
          else if (i == 2)
            {
              derivative[0] = 1.5 - 3.0 * p[0];
              derivative[1] = -2.5 + 3.0 * p[1];
            }
          else if (i == 3)
            {
              derivative[0] = 1.5 - 3.0 * p[0];
              derivative[1] = -0.5 + 3.0 * p[1];
            }
          else
            {
              DEAL_II_NOT_IMPLEMENTED();
            }
          return derivative;
        }
      else if constexpr (order == 2)
        {
          Tensor<2, dim> derivative;
          if (i == 0)
            {
              derivative[0][0] = 3;
              derivative[0][1] = 0;
              derivative[1][0] = 0;
              derivative[1][1] = -3;
            }
          else if (i == 1)
            {
              derivative[0][0] = 3;
              derivative[0][1] = 0;
              derivative[1][0] = 0;
              derivative[1][1] = -3;
            }
          else if (i == 2)
            {
              derivative[0][0] = -3;
              derivative[0][1] = 0;
              derivative[1][0] = 0;
              derivative[1][1] = 3;
            }
          else if (i == 3)
            {
              derivative[0][0] = -3;
              derivative[0][1] = 0;
              derivative[1][0] = 0;
              derivative[1][1] = 3;
            }
          else
            {
              DEAL_II_NOT_IMPLEMENTED();
            }
          return derivative;
        }
      else
        {
          // higher derivatives are all zero
          return {};
        }
    }
  } // namespace PolynomialsRannacherTurekImplementation
} // namespace internal
 
 
 
// template functions
template <int dim>
template <int order>
Tensor<order, dim>
PolynomialsRannacherTurek<dim>::compute_derivative(const unsigned int i,
                                                   const Point<dim>  &p) const
{
  return internal::PolynomialsRannacherTurekImplementation::compute_derivative<
    order>(i, p);
}
 
 
 
template <int dim>
inline Tensor<1, dim>
PolynomialsRannacherTurek<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>
PolynomialsRannacherTurek<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>
PolynomialsRannacherTurek<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>
PolynomialsRannacherTurek<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
PolynomialsRannacherTurek<dim>::name() const
{
  return "RannacherTurek";
}
 
 
DEAL_II_NAMESPACE_CLOSE
 
#endif