[1]王海兵,刘继军.由两层散射体引起的声学散射问题的分裂方法[J].东南大学学报(自然科学版),2011,41(3):652-658.[doi:10.3969/j.issn.1001-0505.2011.03.042]
 Wang Haibing,Liu Jijun.Splitting method for acoustic scattering by a two-layered obstacle[J].Journal of Southeast University (Natural Science Edition),2011,41(3):652-658.[doi:10.3969/j.issn.1001-0505.2011.03.042]
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由两层散射体引起的声学散射问题的分裂方法()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
41
期数:
2011年第3期
页码:
652-658
栏目:
数学、物理学、力学
出版日期:
2011-05-20

文章信息/Info

Title:
Splitting method for acoustic scattering by a two-layered obstacle
作者:
王海兵12刘继军1
(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)
Author(s):
Wang Haibing12Liu Jijun1
(1Department of Mathematics, Southeast University, Nanjing 210096, China)
(2School of Mathematics and Computational Science, Hunan University of Science and Technology, Xiangtan 411201, China)
关键词:
散射两层散射体分裂迭代格式
Keywords:
scattering two-layered scatterer splitting iteration scheme.
分类号:
O175.24
DOI:
10.3969/j.issn.1001-0505.2011.03.042
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.
Abstract:
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.

参考文献/References:

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备注/Memo

备注/Memo:
作者简介:王海兵(1981—),男,博士生;刘继军(联系人),男,博士,教授,博士生导师,jjliu@seu.edu.cn.
基金项目:国家自然科学基金资助项目(11071039).
引文格式: 王海兵,刘继军.由两层散射体引起的声学散射问题的分裂方法[J].东南大学学报:自然科学版,2011,41(3):652-658.[doi:10.3969/j.issn.1001-0505.2011.03.042]
更新日期/Last Update: 2011-05-20