求解一类介质散射问题的特殊解方法  

Particular Solution Method for Solving a Class of Medium Scattering Problem

作　　者：栾天[1] 李双双 张威[1] LUAN Tian;LI Shuangshuang;ZHANG Wei(School of Mathematics and Statistics, Beihua University, Jilin 132013, Jilin Province , China)

机构地区：[1]北华大学数学与统计学院,吉林吉林132013

出　　处：《吉林大学学报（理学版）》2018年第3期561-566,共6页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金青年科学基金(批准号:11701013;11601014);吉林省教育科学"十三五"规划一般项目(批准号:GH170094);吉林省教育厅科学技术研究项目(批准号:JJKH20170022KJ);吉林省自然科学基金(批准号:20160101264JC)

摘　　要：采用特殊解方法,计算求解一类时谐介质散射问题.算法在区域简单剖分的基础上,利用基本解函数近似散射场的局部性态和无穷远处性态,无需将无界域截断为有界域,适用于一般散射体及多个散射体情形,在粗糙网格下便可达到较高精度,并实现快速收敛.数值算例表明了算法的可行性和有效性.A particular solution method was used to compute a class of time harmonic medium scattering problems.Based on a simple partition of the domain,fundamental solutions were selected to approximate the property of the scattered field at local points and infinity.There was no need to cut unbounded domain into a bounded domain.The algorithm was suitable for the general scatterers and multiple scatterers,which could achieve high precision in rough grids and achieve fast convergence.Numerical examples show the feasibility and effectiveness of the algorithm.

关 键 词：HELMHOLTZ方程 位势函数 基本解 介质散射 

分 类 号：O241.82[理学—计算数学]