polynomials_wedge.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_base_polynomials_wedge_h
#define dealii_base_polynomials_wedge_h
 
#include <deal.II/base/config.h>
 
#include <deal.II/base/ndarray.h>
#include <deal.II/base/point.h>
#include <deal.II/base/polynomials_barycentric.h>
#include <deal.II/base/scalar_polynomials_base.h>
#include <deal.II/base/scalar_polynomials_vandermonde_base.h>
#include <deal.II/base/tensor.h>
 
#include <deal.II/grid/reference_cell.h>
 
 
DEAL_II_NAMESPACE_OPEN
 
 
namespace internal
{
  template <int dim>
  std::vector<Point<dim>>
  get_wedge_support_points(const unsigned int degree)
  {
    if constexpr (dim == 3)
      {
        if (degree == 1)
          return {ReferenceCells::Wedge.vertex(0),
                  ReferenceCells::Wedge.vertex(1),
                  ReferenceCells::Wedge.vertex(2),
                  ReferenceCells::Wedge.vertex(3),
                  ReferenceCells::Wedge.vertex(4),
                  ReferenceCells::Wedge.vertex(5)};
        else if (degree == 2)
          return {// vertices
                  ReferenceCells::Wedge.vertex(0),
                  ReferenceCells::Wedge.vertex(1),
                  ReferenceCells::Wedge.vertex(2),
                  ReferenceCells::Wedge.vertex(3),
                  ReferenceCells::Wedge.vertex(4),
                  ReferenceCells::Wedge.vertex(5),
                  // edges
                  0.5 * (ReferenceCells::Wedge.vertex(0) +
                         ReferenceCells::Wedge.vertex(1)),
                  0.5 * (ReferenceCells::Wedge.vertex(1) +
                         ReferenceCells::Wedge.vertex(2)),
                  0.5 * (ReferenceCells::Wedge.vertex(2) +
                         ReferenceCells::Wedge.vertex(0)),
                  0.5 * (ReferenceCells::Wedge.vertex(3) +
                         ReferenceCells::Wedge.vertex(4)),
                  0.5 * (ReferenceCells::Wedge.vertex(4) +
                         ReferenceCells::Wedge.vertex(5)),
                  0.5 * (ReferenceCells::Wedge.vertex(5) +
                         ReferenceCells::Wedge.vertex(3)),
                  0.5 * (ReferenceCells::Wedge.vertex(3) +
                         ReferenceCells::Wedge.vertex(0)),
                  0.5 * (ReferenceCells::Wedge.vertex(1) +
                         ReferenceCells::Wedge.vertex(4)),
                  0.5 * (ReferenceCells::Wedge.vertex(2) +
                         ReferenceCells::Wedge.vertex(5)),
                  // quad midpoints
                  0.25 * (ReferenceCells::Wedge.vertex(0) +
                          ReferenceCells::Wedge.vertex(1) +
                          ReferenceCells::Wedge.vertex(3) +
                          ReferenceCells::Wedge.vertex(4)),
                  0.25 * (ReferenceCells::Wedge.vertex(1) +
                          ReferenceCells::Wedge.vertex(2) +
                          ReferenceCells::Wedge.vertex(4) +
                          ReferenceCells::Wedge.vertex(5)),
                  0.25 * (ReferenceCells::Wedge.vertex(2) +
                          ReferenceCells::Wedge.vertex(0) +
                          ReferenceCells::Wedge.vertex(5) +
                          ReferenceCells::Wedge.vertex(3))};
        else
          DEAL_II_NOT_IMPLEMENTED();
      }
 
    DEAL_II_ASSERT_UNREACHABLE();
    return {};
  }
} // namespace internal
 
 
template <int dim>
class ScalarLagrangePolynomialWedge
  : public ScalarPolynomialsVandermondeBase<dim>
{
public:
  static constexpr unsigned int dimension = dim;
 
  /*
   * Constructor taking the polynomial @p degree and the support points as
   * arguments.
   */
  ScalarLagrangePolynomialWedge(const unsigned int             degree,
                                const std::vector<Point<dim>> &support_points);
 
  /*
   * Legacy constructor taking the polynomial @p degree.
   * Note: only works for degrees one and two.
   */
  ScalarLagrangePolynomialWedge(const unsigned int degree);
 
  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;
};
 
DEAL_II_NAMESPACE_CLOSE
 
#endif