mundy::GaussTriangleEllipsoid< Scalar, Polyhedron, L, BOverA, COverA > Class Template Reference

The three-point Gauss triangle rule on the Polyhedron refined L times and stretched onto the ellipsoid with semi-axes 1, BOverA, COverA, with outward unit normals. More...

#include <GaussTriangleEllipsoid.hpp>

Public Types
using	value_type = Scalar

Static Public Member Functions
static constexpr Kokkos::Array< Scalar, 3 *num_points >	points ()
	The points as (x, y, z) triples: element by element in BEMLIB's order, three per element.
static constexpr Kokkos::Array< Scalar, 3 *num_points >	normals ()
	The outward unit normals of the patches at the points, as (x, y, z) triples in the order of points().
static constexpr Kokkos::Array< Scalar, num_points >	weights ()
	The num_points weights, in the order of points().
template<class Function>
static constexpr auto	integrate (const Function &f)
	sum_i w_i f(x_i, y_i, z_i), approximating the integral of f over the ellipsoid.

Static Public Attributes
static constexpr SpherePolyhedron	polyhedron = Polyhedron
static constexpr unsigned	num_refinements = L
static constexpr double	b_over_a = BOverA
static constexpr double	c_over_a = COverA
static constexpr unsigned	num_elements = static_cast<unsigned>(Polyhedron) << (2 * L)
static constexpr unsigned	num_points = 3 * num_elements

Detailed Description

template<class Scalar, SpherePolyhedron Polyhedron, unsigned L, double BOverA = 1.0, double COverA = 1.0>
class mundy::GaussTriangleEllipsoid< Scalar, Polyhedron, L, BOverA, COverA >

The points, normals, and weights are correctly rounded to Scalar and computed by the compiler, so every member is a constant expression. Like TrapezoidalTorus's rule, it integrates over a unit-scale surface; scale for other sizes.

Member Typedef Documentation

value_type

template<class Scalar, SpherePolyhedron Polyhedron, unsigned L, double BOverA = 1.0, double COverA = 1.0>

using mundy::GaussTriangleEllipsoid< Scalar, Polyhedron, L, BOverA, COverA >::value_type = Scalar

Member Function Documentation

points()

template<class Scalar, SpherePolyhedron Polyhedron, unsigned L, double BOverA = 1.0, double COverA = 1.0>

constexpr Kokkos::Array< Scalar, 3 *num_points > mundy::GaussTriangleEllipsoid< Scalar, Polyhedron, L, BOverA, COverA >::points ( )

inlinestaticconstexpr

normals()

template<class Scalar, SpherePolyhedron Polyhedron, unsigned L, double BOverA = 1.0, double COverA = 1.0>

constexpr Kokkos::Array< Scalar, 3 *num_points > mundy::GaussTriangleEllipsoid< Scalar, Polyhedron, L, BOverA, COverA >::normals ( )

inlinestaticconstexpr

weights()

template<class Scalar, SpherePolyhedron Polyhedron, unsigned L, double BOverA = 1.0, double COverA = 1.0>

constexpr Kokkos::Array< Scalar, num_points > mundy::GaussTriangleEllipsoid< Scalar, Polyhedron, L, BOverA, COverA >::weights ( )

inlinestaticconstexpr

integrate()

template<class Scalar, SpherePolyhedron Polyhedron, unsigned L, double BOverA = 1.0, double COverA = 1.0>

template<class Function>

constexpr auto mundy::GaussTriangleEllipsoid< Scalar, Polyhedron, L, BOverA, COverA >::integrate ( const Function & f )

inlinestaticconstexpr

Member Data Documentation

polyhedron

template<class Scalar, SpherePolyhedron Polyhedron, unsigned L, double BOverA = 1.0, double COverA = 1.0>

SpherePolyhedron mundy::GaussTriangleEllipsoid< Scalar, Polyhedron, L, BOverA, COverA >::polyhedron = Polyhedron

staticconstexpr

num_refinements

template<class Scalar, SpherePolyhedron Polyhedron, unsigned L, double BOverA = 1.0, double COverA = 1.0>

unsigned mundy::GaussTriangleEllipsoid< Scalar, Polyhedron, L, BOverA, COverA >::num_refinements = L

staticconstexpr

b_over_a

template<class Scalar, SpherePolyhedron Polyhedron, unsigned L, double BOverA = 1.0, double COverA = 1.0>

double mundy::GaussTriangleEllipsoid< Scalar, Polyhedron, L, BOverA, COverA >::b_over_a = BOverA

staticconstexpr

c_over_a

template<class Scalar, SpherePolyhedron Polyhedron, unsigned L, double BOverA = 1.0, double COverA = 1.0>

double mundy::GaussTriangleEllipsoid< Scalar, Polyhedron, L, BOverA, COverA >::c_over_a = COverA

staticconstexpr

num_elements

template<class Scalar, SpherePolyhedron Polyhedron, unsigned L, double BOverA = 1.0, double COverA = 1.0>

unsigned mundy::GaussTriangleEllipsoid< Scalar, Polyhedron, L, BOverA, COverA >::num_elements = static_cast<unsigned>(Polyhedron) << (2 * L)

staticconstexpr

num_points

template<class Scalar, SpherePolyhedron Polyhedron, unsigned L, double BOverA = 1.0, double COverA = 1.0>

unsigned mundy::GaussTriangleEllipsoid< Scalar, Polyhedron, L, BOverA, COverA >::num_points = 3 * num_elements

staticconstexpr