由两层散射体引起的声学散射问题的分裂方法  

Splitting method for acoustic scattering by a two-layered obstacle

作　　者：王海兵[1,2] 刘继军[1] 

机构地区：[1]东南大学数学系,南京210096 [2]湖南科技大学数学与计算科学学院,湘潭411201

出　　处：《东南大学学报（自然科学版）》2011年第3期652-658,共7页Journal of Southeast University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11071039)

摘　　要：考虑由一个可穿透的两层散射体引起的声学散射问题.首先,利用位势理论和Fredholm理论,用积分方程证明了正散射问题解的存在性和唯一性.其次,根据散射问题解的积分表示,在散射体的外层介质内,波场由2部分组成,分别对应于散射体的2个界面引起的反射波.基于此,将两层散射体的散射问题分裂成2个耦合的经典透射问题,且证明了该分裂是唯一存在的.为了根据此分裂求得原问题的解,提出了一种解耦的迭代格式,每一步迭代只需要求解2个标准的透射问题,降低了计算的复杂性以及对计算机的存储要求.The acoustic wave scattered by a penetrable two-layered obstacle is considered.Firstly,using the potential theory together with the Fredholm alternative theorem,the solvability of this direct scattering problem is justified by the integral equation method.Then,in terms of the representation of solution,in the outward layer of scatterer,the wave field contains two parts,which respectively correspond to the reflected waves from two interfaces between layers.Based on this result,the original scattering problem is split into two coupled transmission problems.The uniqueness and existence of this splitting are also proven.In order to generate the numerical solution from such a splitting,an iteration scheme to decouple these two coupled scattering problems is proposed.The advantage of this splitting scheme is that only the solvers to the well-known transmission problems are applied,which reduces the computing complexity and the storage requirement for the computer.

关 键 词：散射 两层散射体 分裂 迭代格式 

分 类 号：O175.24[理学—数学]