二维圆域中Poisson方程反源问题的数值方法  

A Numerical Method for Inverse Source Problem of Poisson Equation in 2D Disc Domains

作　　者：王红艳[1] 马富明[1] 

机构地区：[1]吉林大学数学研究所,长春130012

出　　处：《吉林大学学报（理学版）》2010年第2期214-218,共5页Journal of Jilin University:Science Edition

基　　金：国家重点基础研究发展计划973项目基金(批准号:2005CB321701)

摘　　要：讨论二维圆域中Poisson方程的反源问题.根据边值问题解的复函数表示形式及Cauchy积分公式,导出了点源参数与边界条件的代数关系,从而构造了一种代数方法重构单极子源或偶极子源.该方法不需要求解正问题或进行任何迭代,因此更直接、计算量更小.数值结果表明,所给算法是有效的.This paper deals with an inverse source problem of the Poisson equation in a disc domain. Based on the complex expression of the solution to the boundary problem, an algebraic relation between the parameters of the point sources and the boundary conditions was deduced by means of the Cauchy integral formula. Then an algebraic numerical algorithm was proposed to reconstruct the dipoles or monopoles. Since the algorithm does not need solving the forward problem or any iterative procedure, it is direct and reduces the calculation amount. For the purpose of verifying the validity of the algorithm, numerical examples were provided.

关 键 词：反源问题 柯西积分公式 极点 支点 单极子源 偶极子源 

分 类 号：O241.82[理学—计算数学]