Inverse random source scattering for the Helmholtz equation in inhomogeneous media

doi:10.1088/1361-6420/aa99d2

	Inverse random source scattering for the Helmholtz equation in inhomogeneous media
	Li, Ming 1; Chen, Chuchu2 ; Li, Peijun 3
	2018
发表期刊	INVERSE PROBLEMS
ISSN	0266-5611
卷号	34 期号:1 页码:19
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.
关键词	inverse source scattering problem the Helmholtz equation stochastic partial differential equation
DOI	10.1088/1361-6420/aa99d2
语种	英语
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
WOS类目	Mathematics, Applied ; Physics, Mathematical
WOS记录号	WOS:000417912700002
出版者	IOP PUBLISHING LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/444
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.