格林函数的高斯正交生成:一种随机算法

Conference Proceedings. IEEE Canadian Conference on Electrical and Computer Engineering (Cat. No.98TH8341) Pub Date : 1998-05-24 DOI:10.1109/CCECE.1998.685582

H. H. Pham, A. Nathan

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引用次数: 3

摘要

本文报道了格林函数的指数积分表示生成高斯正交的一种随机方案。这些高斯正交构成了基于指数展开的方法的基础，该方法先前已被开发用于在三维空间中快速准确地评估势场及其梯度。给定/sup 1/// /sub r/近似值的期望精度，这里提出的技术可以生成尺寸尽可能小的指数展开。它利用了标准的勒让德-高斯和切比雪夫-高斯正交，并且不需要求解一个大型的非线性方程组。

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Generating Gauss quadratures for Green's function /sup 1///sub r/: a randomized algorithm

We report a randomized scheme for generating Gauss quadratures for an exponential integral representation of the Green's function /sup 1///sub r/. These Gauss quadratures form the basis of the exponential-expansion-based method, which has previously been developed for rapid and accurate evaluation of the potential field and its gradient in three dimensions. Given a desired degree of accuracy on the approximation of /sup 1///sub r/, the technique proposed here enables generation of exponential expansion with sizes as small as possible. It makes use of the standard Legendre-Gauss and Chebychev-Gauss quadratures, and does not require solving a large system of non-linear equations.

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Conference Proceedings. IEEE Canadian Conference on Electrical and Computer Engineering (Cat. No.98TH8341)

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