Inverse Fluid-solid Interaction Scattering Problem Using Phased and Phaseless Far Field Data

doi:10.1007/s10255-020-0914-7

CORC > 数学与系统科学研究院 > 中国科学院数学与系统科学研究院 > 应用数学研究所

	Inverse Fluid-solid Interaction Scattering Problem Using Phased and Phaseless Far Field Data
	Ji, Xia 1; Jia, Yun-fei 2,3; Liu, Xiao-dong 3
刊名	ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES
	2020
卷号	36 期号:1 页码:74-94
关键词	fluid-solid interaction scattering direct sampling method far field pattern phaseless phase retrieval
ISSN号	0168-9673
DOI	10.1007/s10255-020-0914-7
英文摘要	We consider the inverse fluid-solid interaction scattering of incident plane wave from the knowledge of the phased and phaseless far field patterns. For the phased data, one direct sampling method for location and shape reconstruction is proposed. Only inner product is involved in the computation, which makes it very simple and fast to be implemented. With the help of the factorization of the far field operator, we give a lower bound of the proposed indicator functional for the sampling points inside the elastic body. While for the sampling points outside, we show that the indicator functional decays like the Bessel function as the points go away from the boundaries of the elastic body. We also show that the proposed indicator functional continuously dependents on the far field patterns, which further implies that the novel sampling method is extremely stable with respect to data error. For the phaseless data, to overcome the translation invariance, we consider the scattering of point sources simultaneously. By adding a reference sound-soft obstacle into the scattering system, we show some uniqueness results with phaseless far field data. Numerically, we introduce a phase retrieval algorithm to retrieve the phased data without the additional obstacle. The novel phase retrieval algorithm can also be combined with the sampling method for phased data. We also design two novel direct sampling methods using the phaseless data directly. Finally, some numerical simulations in two dimensions are conducted with noisy data, and the results further verify the effectiveness and robustness of the proposed numerical methods.
资助项目	National Natural Science Foundation of China[11571355] ; National Natural Science Foundation of China[11971701] ; National Natural Science Foundation of China[91630313] ; National Natural Science Foundation of China[11971468] ; National Centre for Mathematics and Interdisciplinary Sciences, CAS ; Youth Innovation Promotion Association, CAS
WOS研究方向	Mathematics
语种	英语
出版者	SPRINGER HEIDELBERG
WOS记录号	WOS:000504613100006
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/50522]
专题	应用数学研究所
通讯作者	Liu, Xiao-dong
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Ji, Xia,Jia, Yun-fei,Liu, Xiao-dong. Inverse Fluid-solid Interaction Scattering Problem Using Phased and Phaseless Far Field Data[J]. ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES,2020,36(1):74-94.
APA	Ji, Xia,Jia, Yun-fei,&Liu, Xiao-dong.(2020).Inverse Fluid-solid Interaction Scattering Problem Using Phased and Phaseless Far Field Data.ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES,36(1),74-94.
MLA	Ji, Xia,et al."Inverse Fluid-solid Interaction Scattering Problem Using Phased and Phaseless Far Field Data".ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES 36.1(2020):74-94.