求解散射问题快速多极算法截断误差的一种新的估计  

A NEW ESTIMATION OF THE TRUNCATION ERRORS IN THE FAST MULTIPOLE METHOD FOR SCATTERING PROBLEMS

作　　者：李瑞蓉 孟文辉 Li Ruirong;Meng Wenhui(School of Mathematics,Northwest University,Xi'an 710127,China)

机构地区：[1]西北大学数学学院,西安710127

出　　处：《数值计算与计算机应用》2022年第4期415-424,共10页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(11201373)资助。

摘　　要：快速多极算法(FMM)是处理大规模多粒子系统的一种有效的快速算法.在应用快速多极算法求解散射问题时,相关的展开式和转换式都使用了Bessel函数的Graf加法定理。在实际计算中,算法的误差是通过截断Graf加法定理产生的.本文针对快速多极算法误差的特征,给出了Graf加法定理截断误差的一个新的估计,该结果比已有的结果形式更简单且逼近效果更好,这就使得本文的结果能够更好地应用于求解散射问题的快速多极算法中.数值实验验证了本文结果的有效性和精确性.The fast multipole method(FMM)is an efficient and fast algorithm for large-scale multi-particle systems.In the FMM for solving scattering problems,the related expansion and transformation expressions are based on Graf's addition theorem for Bessel functions.The error of the algorithm in practical calculation is introduced by truncating Graf's addition theorem.In this paper,a new estimate for the truncation errors of Graf's addition theorem is given according to characteristics of errors of the FMM.The results have simpler forms and better approximation effects than existing results,which makes them can be better applied to the FMM for solving scattering problems.Numerical experiments verify the effectiveness and accuracy of ourresults.

关 键 词：HELMHOLTZ方程 快速多极算法 截断误差 BESSEL函数 Graf加法定理 

分 类 号：O241.8[理学—计算数学]