Fast multipole method for singular integral equations of second kind

Advances in Difference Equations

Qinghua Wu¹  Shuhuang Xiang² 

[1] Department of Mathematics and Computational Science, Hunan University of Science and Engineering, Yongzhou, P.R. China;School of Mathematics and Statistics, Central South University, Changsha, P.R. China

关键词: singular integral equation;    boundary element method;    fast multipole method;    Cauchy principal value;    finite-part integral;   

DOI  :  10.1186/s13662-015-0515-6

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

This paper explores the numerical methods for a singular integral equation (SIE), which arise in the study of various problems of mathematical physics and engineering. The idea behind the boundary element method (BEM) is used to discretize the SIE. The fast multipole method (FMM), which is a very efficient and popular algorithm for the rapid solution of boundary value problems, is used to accelerate the BEM solutions of SIE. The effectiveness and accuracy of the proposed method are tested by numerical examples.

【 授权许可】

CC BY