polynomials_simplex.h

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// -----------------------------------------------------------------------------
//
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception OR LGPL-2.1-or-later
// Copyright (C) 2021 - 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_polynomials_simplex_h
#define dealii_polynomials_simplex_h
 
#include <deal.II/base/config.h>
 
#include <deal.II/base/point.h>
#include <deal.II/base/scalar_polynomials_vandermonde_base.h>
#include <deal.II/base/tensor.h>
 
#include <deal.II/lac/full_matrix.h>
 
DEAL_II_NAMESPACE_OPEN
 
template <int dim>
class ScalarLagrangePolynomialSimplex
  : public ScalarPolynomialsVandermondeBase<dim>
{
public:
  static constexpr unsigned int dimension = dim;
 
  /*
   * Constructor taking the polynomial @p degree, the number of polynomials
   * @p n_dofs and the support points as input.
   */
  ScalarLagrangePolynomialSimplex(
    const unsigned int             degree,
    const std::vector<Point<dim>> &support_points);
 
  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;
 
private:
  double
  evaluate_orthogonal_basis_function_by_degree(
    const unsigned int i,
    const unsigned int j,
    const unsigned int k,
    const Point<dim>  &p) const override;
 
  double
  evaluate_orthogonal_basis_function(const unsigned int i,
                                     const Point<dim>  &p) const override;
 
  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 override;
 
  Tensor<1, dim>
  evaluate_orthogonal_basis_derivative(const unsigned int i,
                                       const Point<dim>  &p) const override;
 
  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 override;
 
  virtual Tensor<2, dim>
  evaluate_orthogonal_basis_2nd_derivative(const unsigned int i,
                                           const Point<dim>  &p) const override;
};
 
 
DEAL_II_NAMESPACE_CLOSE
 
#endif