ref_triangle.hpp

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// Copyright (C) 2025 Tiago V. L. Amorim (@tiagovla)
//
// This file is part of oiseau (https://github.com/tiagovla/oiseau)
//
// SPDX-License-Identifier: GPL-3.0-or-later
 
#pragma once
 
#include "oiseau/dg/nodal/ref_element.hpp"
#include "xtensor/core/xtensor_forward.hpp"

 
namespace oiseau::dg::nodal {

class RefTriangle : public RefElement {
 public:
  explicit RefTriangle(unsigned order);

  static xt::xarray<double> basis_function(const xt::xarray<double>& ab, int i, int j);

  static xt::xarray<double> grad_basis_function(const xt::xarray<double>& ab, int i, int j);
 
 private:
  xt::xarray<double> vandermonde(const xt::xarray<double>& rs) const;

  xt::xarray<double> grad_vandermonde(const xt::xarray<double>& rs) const;

  xt::xarray<double> grad_operator(const xt::xarray<double>& v, const xt::xarray<double>& gv) const;
};
 
namespace detail {

xt::xarray<double> rs_to_ab(const xt::xarray<double>& rs);

xt::xarray<double> generate_triangle_nodes(unsigned order);

xt::xarray<double> equilateral_xy_to_rs(const xt::xarray<double>& xy);

xt::xarray<double> warp_factor(unsigned order, const xt::xarray<double>& rs);
 
}  // namespace detail
}  // namespace oiseau::dg::nodal