GaussJacobiQuadrature.h

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// Class GaussJacobiQuadrature
//   The GaussJacobiQuadrature class. This is a class representing a Gauss-Jacobi quadrature
//   The algoirthm in computeNodesAndWeights is based on the LehrFEM++ library.
//   https://craffael.github.io/lehrfempp/gauss__quadrature_8cc_source.html
 
#ifndef IPPL_GAUSSJACOBIQUADRATURE_H
#define IPPL_GAUSSJACOBIQUADRATURE_H
 
#include "FEM/Quadrature/Quadrature.h"
 
namespace ippl {
 
    enum InitialGuessType {
        Chebyshev,
        LehrFEM,
    };

    template <typename T, unsigned NumNodes1D, typename ElementType>
    class GaussJacobiQuadrature : public Quadrature<T, NumNodes1D, ElementType> {
    public:
        // a higher precision floating point number type used for the computation
        // of the quadrature nodes and weights
        using scalar_t = double;  // might be equivalant to double, depending on compiler

        GaussJacobiQuadrature(const ElementType& ref_element, const T& alpha, const T& beta,
                              const size_t& max_newton_itersations = 10,
                              const size_t& min_newton_iterations  = 1);

        void computeNodesAndWeights() override;

        scalar_t getChebyshevNodes(const size_t& i) const;  // FIXME maybe move somewhere else?
 
    private:
        scalar_t getLehrFEMInitialGuess(
            const size_t& i, const Vector<scalar_t, NumNodes1D>& integration_nodes) const;
 
        const T alpha_m;
        const T beta_m;
 
        const size_t max_newton_iterations_m;
        const size_t min_newton_iterations_m;
    };

    template <typename T, unsigned NumNodes1D, typename ElementType>
    class GaussLegendreQuadrature : public GaussJacobiQuadrature<T, NumNodes1D, ElementType> {
    public:
        GaussLegendreQuadrature(const ElementType& ref_element,
                                const size_t& max_newton_itersations = 10,
                                const size_t& min_newton_iterations  = 1)
            : GaussJacobiQuadrature<T, NumNodes1D, ElementType>(
                ref_element, 0.0, 0.0, max_newton_itersations, min_newton_iterations) {}
    };

    template <typename T, unsigned NumNodes1D, typename ElementType>
    class ChebyshevGaussQuadrature : public GaussJacobiQuadrature<T, NumNodes1D, ElementType> {
    public:
        ChebyshevGaussQuadrature(const ElementType& ref_element,
                                 const size_t& max_newton_itersations = 10,
                                 const size_t& min_newton_iterations  = 1)
            : GaussJacobiQuadrature<T, NumNodes1D, ElementType>(
                ref_element, -0.5, -0.5, max_newton_itersations, min_newton_iterations) {}
    };
 
}  // namespace ippl
 
#include "FEM/Quadrature/GaussJacobiQuadrature.hpp"
 
#endif