Inverse random source scattering for the Helmholtz equation in inhomogeneous media
文献类型：期刊论文
| 作者 | Li, Ming1; Chen, Chuchu2 ; Li, Peijun3
|
| 刊名 | INVERSE PROBLEMS
 |
| 出版日期 | 2018 |
| 卷号 | 34期号:1页码:19 |
| 关键词 | inverse source scattering problem the Helmholtz equation stochastic partial differential equation |
| ISSN号 | 0266-5611 |
| DOI | 10.1088/1361-6420/aa99d2 |
| 英文摘要 | This paper is concerned with an inverse random source scattering problem in an inhomogeneous background medium. The wave propagation is modeled by the stochastic Helmholtz equation with the source driven by additive white noise. The goal is to reconstruct the statistical properties of the random source such as the mean and variance from the boundary measurement of the radiated random wave field at multiple frequencies. Both the direct and inverse problems are considered. We show that the direct problem has a unique mild solution by a constructive proof. For the inverse problem, we derive Fredholm integral equations, which connect the boundary measurement of the radiated wave field with the unknown source function. A regularized block Kaczmarz method is developed to solve the ill-posed integral equations. Numerical experiments are included to demonstrate the effectiveness of the proposed method. |
| 资助项目 | National Natural Science Foundation of China[11771321] ; National Natural Science Foundation of China[91130003] ; National Natural Science Foundation of China[11021101] ; National Natural Science Foundation of China[11290142] ; NSF[DMS-1151308] |
| WOS研究方向 | Mathematics ; Physics |
| 语种 | 英语 |
| WOS记录号 | WOS:000417912700002 |
| 出版者 | IOP PUBLISHING LTD |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/443]  |
| 专题 | 计算数学与科学工程计算研究所 |
| 通讯作者 | Li, Peijun |
| 作者单位 | 1.Taiyuan Univ Technol, Coll Data Sci, Taiyuan 030024, Shanxi, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China 3.Purdue Univ, Dept Math, W Lafayette, IN 47907 USA |
| 推荐引用方式 GB/T 7714 | Li, Ming,Chen, Chuchu,Li, Peijun. Inverse random source scattering for the Helmholtz equation in inhomogeneous media[J]. INVERSE PROBLEMS,2018,34(1):19. |
| APA | Li, Ming,Chen, Chuchu,&Li, Peijun.(2018).Inverse random source scattering for the Helmholtz equation in inhomogeneous media.INVERSE PROBLEMS,34(1),19. |
| MLA | Li, Ming,et al."Inverse random source scattering for the Helmholtz equation in inhomogeneous media".INVERSE PROBLEMS 34.1(2018):19. |
入库方式： OAI收割
来源：数学与系统科学研究院
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