一种新的三维位势问题多极边界元离散方法

A new kind of discrete method with FM-BEM about 3D potential problem

应用快速多极展开法将三维位势问题的边界方程离散.但是由于在边界方程基本解中,含有奇异项1/r,其影响了多极展开(FMM)的应用,但是利用拉普拉斯变换,可以转换为指数形式序列.这种方法改善了多极展开的奇异性,得到了新的离散解析式,为多极边界元在工程应用提供了理论分析.

In this paper, discrete problem of the boundary integral equation about potential problem is solved by applying fast multipole expansion. In the boundary equation, basic solutions contain singular term 1/r, which influences the application of multipole expansion method. But it can be conversed to exponential series by Laplace transformation. This method improves the original FMM, gets new discrete equality and provides theory analysis for applying FMM in engineering application.