NAME

sc::LebedevLaikovIntegrator - An implementation of a Lebedev angular integrator.

SYNOPSIS

#include <integrator.h>

Inherits sc::AngularIntegrator.

Public Member Functions

LebedevLaikovIntegrator (const Ref< KeyVal > &)
Construct a LebedevLaikovIntegrator using the given KeyVal input. LebedevLaikovIntegrator (StateIn &)
LebedevLaikovIntegrator (int)
void save_data_state (StateOut &)
Save the base classes (with save_data_state) and the members in the same order that the StateIn CTOR initializes them. int nw (void) const
int num_angular_points (double r_value, int ir)
double angular_point_cartesian (int iangular, double r, SCVector3 &integration_point) const
void print (std::ostream &=ExEnv::out0()) const
Print the object.

Protected Member Functions

void init (int n)

Protected Attributes

int npoint_
double * x_
double * y_
double * z_
double * w_

Additional Inherited Members

Detailed Description

An implementation of a Lebedev angular integrator.

It uses code written by Dr. Dmitri N. Laikov.

This can generate grids with the following numbers of points: 6, 14, 26, 38, 50, 74, 86, 110, 146, 170, 194, 230, 266, 302, 350, 386, 434, 482, 530, 590, 650, 698, 770, 830, 890, 974, 1046, 1118, 1202, 1274, 1358, 1454, 1538, 1622, 1730, 1814, 1910, 2030, 2126, 2222, 2354, 2450, 2558, 2702, 2810, 2930, 3074, 3182, 3314, 3470, 3590, 3722, 3890, 4010, 4154, 4334, 4466, 4610, 4802, 4934, 5090, 5294, 5438, 5606, and 5810.

V.I. Lebedev, and D.N. Laikov 'A quadrature formula for the sphere of the 131st algebraic order of accuracy' Doklady Mathematics, Vol. 59, No. 3, 1999, pp. 477-481.

V.I. Lebedev 'A quadrature formula for the sphere of 59th algebraic order of accuracy' Russian Acad. Sci. Dokl. Math., Vol. 50, 1995, pp. 283-286.

V.I. Lebedev, and A.L. Skorokhodov 'Quadrature formulas of orders 41, 47, and 53 for the sphere' Russian Acad. Sci. Dokl. Math., Vol. 45, 1992, pp. 587-592.

V.I. Lebedev 'Spherical quadrature formulas exact to orders 25-29' Siberian Mathematical Journal, Vol. 18, 1977, pp. 99-107.

V.I. Lebedev 'Quadratures on a sphere' Computational Mathematics and Mathematical Physics, Vol. 16, 1976, pp. 10-24.

V.I. Lebedev 'Values of the nodes and weights of ninth to seventeenth order Gauss-Markov quadrature formulae invariant under the octahedron group with inversion' Computational Mathematics and Mathematical Physics, Vol. 15, 1975, pp. 44-51.

Constructor & Destructor Documentation

sc::LebedevLaikovIntegrator::LebedevLaikovIntegrator (const Ref< KeyVal > &)

Construct a LebedevLaikovIntegrator using the given KeyVal input. The n keyword gives the number of angular points. The default is 302.

Member Function Documentation

double sc::LebedevLaikovIntegrator::angular_point_cartesian (int iangular, double r, SCVector3 & integration_point) const [virtual]

Implements sc::AngularIntegrator.

Author

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