CSpace  > 计算数学与科学工程计算研究所
INVERSE RANDOM SOURCE SCATTERING FOR ELASTIC WAVES
Bao, Gang1; Chen, Chuchu2; Li, Peijun3
2017
Source PublicationSIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN0036-1429
Volume55Issue:6Pages:2616-2643
AbstractThis paper is concerned with the direct and inverse random source scattering problems for elastic waves, where the source is assumed to be driven by an additive white noise. Given the source, the direct problem is to determine the displacement of the random wave field. The inverse problem is to reconstruct the mean and variance of the random source from the boundary measurement of the wave field at multiple frequencies. The direct problem is shown to have a unique mild solution by using a constructive proof. Based on the explicit mild solution, Fredholm integral equations of the first kind are deduced for the inverse problem. The regularized block Kaczmarz method is developed to solve the ill-posed integral equations. The convergence is proved for the method. Numerical experiments are shown to demonstrate the effectiveness of the proposed method.
Keywordinverse source scattering problem elastic wave equation stochastic partial differential equation Fredholm integral equation
DOI10.1137/16M1088922
Language英语
Funding ProjectKey Project of the Major Research Plan of NSFC[91130004] ; NSFC A3 project[11421110002] ; NSFC Tianyuan project[11426235] ; NSFC Tianyuan project[11526211] ; NSFC Innovative Group Fund[11621101] ; Zhejiang University ; NSFC[91130003] ; NSFC[11021101] ; NSFC[11290142] ; NSF grant[DMS-1151308]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000418663500005
PublisherSIAM PUBLICATIONS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/27089
Collection计算数学与科学工程计算研究所
Corresponding AuthorLi, Peijun
Affiliation1.Zhejiang Univ, Sch Math Sci, Hangzhou 310027, Zhejiang, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China
3.Purdue Univ, Dept Math, W Lafayette, IN 47907 USA
Recommended Citation
GB/T 7714
Bao, Gang,Chen, Chuchu,Li, Peijun. INVERSE RANDOM SOURCE SCATTERING FOR ELASTIC WAVES[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2017,55(6):2616-2643.
APA Bao, Gang,Chen, Chuchu,&Li, Peijun.(2017).INVERSE RANDOM SOURCE SCATTERING FOR ELASTIC WAVES.SIAM JOURNAL ON NUMERICAL ANALYSIS,55(6),2616-2643.
MLA Bao, Gang,et al."INVERSE RANDOM SOURCE SCATTERING FOR ELASTIC WAVES".SIAM JOURNAL ON NUMERICAL ANALYSIS 55.6(2017):2616-2643.
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