Helmholtz方程问题的快速多极边界元求解方法  

Fast multipole boundary element method for Helmholtz equation problems

作　　者：于海源[1] 陈一鸣[1] 于春肖[1] 

机构地区：[1]燕山大学理学院,河北秦皇岛066004

出　　处：《天津工业大学学报》2012年第6期85-88,共4页Journal of Tiangong University

基　　金：河北省自然科学基金项目(A2011203020);河北省高等学校科学技术研究重点项目(ZD2010116)

摘　　要：为了改善传统边界元在求解大规模Helmholtz方程的实际问题时计算效率低、存储量大的缺点,针对快速多极边界元法求解Helmholtz方程进行了理论分析.通过对二维和三维Helmholtz方程的基本解的核函数进行多极展开和局部展开,得到了相应的展开定理,并基于展开定理分别推导了二维和三维问题Helmholtz方程的快速多极边界元计算公式,给出了快速多极边界元法求解Helmholtz方程的主要计算步骤.In order to overcome the difficulties of low computational efficiency and high memory requirement in the conven-tional boundary element method for solving large-scale Helmhohz equation problems, a fast muhipole boundary element method for the problems of Helmholtz equation is presented. Two theorems are obtained based on the multipole expansion and the local expansion of the boundary element method fundamental solutions＇Kernel func-tion. What＇s more, the basic formulas and the main steps of the fast muhipole boundary element method are de-scribed for 2D and 3D Helmhohz equation problems.

关 键 词：快速多极边界元法 HELMHOLTZ方程 基本解 

分 类 号：O241.4[理学—计算数学]