scalar_polynomials_vandermonde_base.h

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// -----------------------------------------------------------------------------
//
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception OR LGPL-2.1-or-later
// Copyright (C) 2020 - 2026 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_scalar_polynomials_vandermonde_base_h
#define dealii_scalar_polynomials_vandermonde_base_h
 
 
#include <deal.II/base/config.h>
 
#include <deal.II/base/point.h>
#include <deal.II/base/scalar_polynomials_base.h>
#include <deal.II/base/tensor.h>
 
#include <deal.II/lac/full_matrix.h>
 
DEAL_II_NAMESPACE_OPEN
 
template <int dim>
class ScalarPolynomialsVandermondeBase : public ScalarPolynomialsBase<dim>
{
public:
  ScalarPolynomialsVandermondeBase(const unsigned int degree,
                                   const unsigned int n_dofs);
 
  /*
   * Virtual destructor. Makes sure that pointers to this class are deleted
   * properly.
   */
  virtual ~ScalarPolynomialsVandermondeBase() = default;
 
  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;
 
  Tensor<1, dim>
  compute_1st_derivative(const unsigned int i,
                         const Point<dim>  &p) const override;
 
  Tensor<2, dim>
  compute_2nd_derivative(const unsigned int i,
                         const Point<dim>  &p) const override;
 
  Tensor<3, dim>
  compute_3rd_derivative(const unsigned int i,
                         const Point<dim>  &p) const override;
 
  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;
 
protected:
  FullMatrix<double> vandermonde_matrix_inverse;
 
  /*
   * Evaluate the modal basis at all support points @p support_points to construct
   * the Vandermonde matrix and invert it.
   */
  void
  reinit(const std::vector<Point<dim>> &support_points);
 
  virtual double
  evaluate_orthogonal_basis_function_by_degree(const unsigned int i,
                                               const unsigned int j,
                                               const unsigned int k,
                                               const Point<dim>  &p) const = 0;
 
  virtual double
  evaluate_orthogonal_basis_function(const unsigned int i,
                                     const Point<dim>  &p) const = 0;
 
  virtual Tensor<1, dim>
  evaluate_orthogonal_basis_derivative_by_degree(const unsigned int i,
                                                 const unsigned int j,
                                                 const unsigned int k,
                                                 const Point<dim> &p) const = 0;
 
  virtual Tensor<1, dim>
  evaluate_orthogonal_basis_derivative(const unsigned int i,
                                       const Point<dim>  &p) const = 0;
 
  virtual Tensor<2, dim>
  evaluate_orthogonal_basis_2nd_derivative_by_degree(const unsigned int i,
                                                     const unsigned int j,
                                                     const unsigned int k,
                                                     const Point<dim> &p) const;
 
  virtual Tensor<2, dim>
  evaluate_orthogonal_basis_2nd_derivative(const unsigned int i,
                                           const Point<dim>  &p) const;
};
 
 
 
template <int dim>
template <int order>
Tensor<order, dim>
ScalarPolynomialsVandermondeBase<dim>::compute_derivative(
  const unsigned int i,
  const Point<dim>  &p) const
{
  Tensor<order, dim> der;
 
  if constexpr (order == 1)
    {
      const auto grad = compute_grad(i, p);
 
      for (unsigned int i = 0; i < dim; ++i)
        der[i] = grad[i];
    }
  else if (order == 2)
    {
      const auto grad_grad = compute_grad_grad(i, p);
 
      for (unsigned int i = 0; i < dim; ++i)
        for (unsigned int e = 0; e < dim; ++e)
          der[i][e] = grad_grad[i][e];
    }
  else
    DEAL_II_NOT_IMPLEMENTED();
 
  return der;
}
 
DEAL_II_NAMESPACE_CLOSE
 
#endif