Numerical integration over a spherical shell

Abstract A numerical integration rule is given for the calculation of three dimensional integrals on a spherical coordinate grid: integrals are considered as a weighted sum of integrand values. The program computes the points of the grid where the functions are to be determined and the associated weights. Two examples of integration are performed to normalize and integrate a numerical function. Title of program: R3DGL Catalogue Id: ABFT_v1_0 Nature of problem A numerical integration rule is given for the calculation of three dimensional integrals on a spherical coordinate grid: integrals are considered as a weighted sum of integrand values. The program computes the points of the grid where the functions are to be determined and the associated weights. An example of integration is performed to normalize a numerical function. Versions of this program held in the CPC repository in Mendeley Data ABFT_v1_0; R3DGL; 10.1016/0010-4655(89)90115-X This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)摘要 本文提出了适用于球坐标系下三维积分计算的数值积分法则：积分可表示为被积函数值的加权和。本程序可计算需要求解函数值的网格点及其对应权重。本文通过两个积分示例完成了数值函数的归一化与积分运算。 程序名称：R3DGL 目录编号：ABFT_v1_0 问题性质 本文提出了适用于球坐标系下三维积分计算的数值积分法则：积分可表示为被积函数值的加权和。本程序可计算需要求解函数值的网格点及其对应权重。本文通过一个积分示例完成了数值函数的归一化处理。 本程序在门德雷数据（Mendeley Data）中的CPC存储库内的版本为：ABFT_v1_0；R3DGL；10.1016/0010-4655(89)90115-X 本程序源自贝尔法斯特女王大学维护的CPC程序库（1969-2019）