基于积分核级数展开的多极边界元法及其截断误差分析  

FM-BEM based on series expansion of integral kernel and its error analysis

作　　者：于春肖[1] 苑润浩[1] 于海源[1] 王慧倩[1] 

机构地区：[1]燕山大学理学院,河北秦皇岛066004

出　　处：《燕山大学学报》2013年第3期254-259,共6页Journal of Yanshan University

基　　金：河北省自然科学基金资助项目(A2011203020);河北省高等学校科学技术研究重点资助项目(ZD2010116);秦皇岛市科学技术研究与发展计划项目(2012021A046)

摘　　要：对于二维Helmholtz方程问题,本文提出一种基于积分核级数展开的多极边界元方法,推导证明了二维Helmholtz方程的多极展开定理,给出了多极边界元法计算公式和计算过程,分析了截断误差,说明截断误差可由截断项数控制,并给出一个可广泛应用于实际计算的截断项数的近似表达式。A kind of Fast Multipole Boundary Element Method（FM-BEM） based on series expansion of integral kernel is proposed to solve two-dimensional（2-D） Helmholtz equation problems in this paper.A theorem of multipole expansion is derived and proved for the fundamental solution.Numerical formulas and computational process of the FM-BEM are obtained for 2-D Helmholtz equation problems.The truncation error is analyzed and proved to be controlled by a truncation number.A refined approximate expression of is finally derived for practical science and engineering computation.

关 键 词：多极边界元法 HELMHOLTZ方程 误差分析 截断项数 

分 类 号：O241[理学—计算数学] O221.2[理学—数学]