GaussJacobi.hpp

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#pragma once
 
#include <array>
#include "QuadratureBase.hpp"
 
namespace DNDS::Geom::Elem
{
    // ===================================================================
    // Gauss-Jacobi Quadrature on [0, 1] with weight (1-z)^2
    // ===================================================================
    // These are used for pyramid quadrature in the z-direction.
    // The pyramid is parameterized with z in [0,1] and (x,y) in the base
    // scaled by (1-z). The Jacobian factor introduces a (1-z)^2 weight.
    //
    // Parameters: alpha = 2, beta = 0 (Jacobi polynomials)
    // Reference interval: [0, 1]
    //
    // Data format: [2][n] array where:
    //   [0][i] = quadrature point (zi) in [0, 1]
    //   [1][i] = quadrature weight (wi)
    // ===================================================================
 
    /// Gauss-Jacobi (alpha=2, beta=0) with 1 point
    namespace detail
    {
        static constexpr std::array<std::array<t_real, 1>, 2> GaussJacobi_01A2B0_1{{{{0.250000000000000}},
                                                                                    {{0.333333333333333}}}};
 
        /// Gauss-Jacobi (alpha=2, beta=0) with 2 points
        static constexpr std::array<std::array<t_real, 2>, 2> GaussJacobi_01A2B0_2{{{{0.122514822655441, 0.544151844011225}},
                                                                                    {{0.232547451253508, 0.100785882079825}}}};
 
        /// Gauss-Jacobi (alpha=2, beta=0) with 3 points
        static constexpr std::array<std::array<t_real, 3>, 2> GaussJacobi_01A2B0_3{{{{0.072994024073150, 0.347003766038352, 0.705002209888499}},
                                                                                    {{0.157136361064887, 0.146246269259866, 0.029950703008581}}}};
 
        /// Gauss-Jacobi (alpha=2, beta=0) with 4 points
        static constexpr std::array<std::array<t_real, 4>, 2> GaussJacobi_01A2B0_4{{{{0.048500549446997, 0.238600737551862, 0.517047295104367, 0.795851417896773}},
                                                                                    {{0.110888415611278, 0.143458789799214, 0.068633887172923, 0.010352240749918}}}};
 
        /// Gauss-Jacobi (alpha=2, beta=0) with 5 points
        static constexpr std::array<std::array<t_real, 5>, 2> GaussJacobi_01A2B0_5{{{{0.034578939918215, 0.173480320771696, 0.389886387065519, 0.634333472630887, 0.851054212947016}},
                                                                                    {{0.081764784285771, 0.126198961899911, 0.089200161221590, 0.032055600722962, 0.004113825203099}}}};
 
    } // namespace detail
} // namespace DNDS::Geom::Elem