KMS Of Academy of mathematics and systems sciences, CAS
| Direct sampling methods for inverse elastic scattering problems | |
Ji, Xia1 ; Liu, Xiaodong2; Xi, Yingxia3
| |
| 2018-03-01 | |
| Source Publication | INVERSE PROBLEMS
 |
| ISSN | 0266-5611 |
| Volume | 34Issue:3Pages:22 |
| Abstract | We consider the inverse elastic scattering of incident plane compressional and shear waves from the knowledge of the far field patterns. Specifically, three direct sampling methods for location and shape reconstruction are proposed using the different component of the far field patterns. Only inner products are involved in the computation, thus the novel sampling methods are 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 functionals for sampling points inside the scatterers. While for the sampling points outside the scatterers, we show that the indicator functionals decay like the Bessel functions as the sampling point goes away from the boundary of the scatterers. We also show that the proposed indicator functionals continuously dependent on the far field patterns, which further implies that the novel sampling methods are extremely stable with respect to data error. For the case when the observation directions are restricted into the limited aperture, we firstly introduce some data retrieval techniques to obtain those data that can not be measured directly and then use the proposed direct sampling methods for location and shape reconstructions. Finally, some numerical simulations in two dimensions are conducted with noisy data, and the results further verify the effectiveness and robustness of the proposed sampling methods, even for multiple multiscale cases and limited-aperture problems. |
| Keyword | elastic scattering sampling method far field pattern limited-aperture problem |
| DOI | 10.1088/1361-6420/aaa996 |
| Language | 英语 |
| Funding Project | NNSF of China[11271018] ; NNSF of China[91630313] ; NNSF of China[11571355] ; National Centre for Mathematics and Interdisciplinary Sciences, CAS ; Youth Innovation Promotion Association, CAS |
| WOS Research Area | Mathematics ; Physics |
| WOS Subject | Mathematics, Applied ; Physics, Mathematical |
| WOS ID | WOS:000424903900001 |
| Publisher | IOP PUBLISHING LTD |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/450 |
| Collection | 计算数学与科学工程计算研究所 应用数学研究所 |
| Corresponding Author | Ji, Xia |
| Affiliation | 1.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Beijing 100190, Peoples R China |
| Recommended Citation GB/T 7714 | Ji, Xia,Liu, Xiaodong,Xi, Yingxia. Direct sampling methods for inverse elastic scattering problems[J]. INVERSE PROBLEMS,2018,34(3):22. |
| APA | Ji, Xia,Liu, Xiaodong,&Xi, Yingxia.(2018).Direct sampling methods for inverse elastic scattering problems.INVERSE PROBLEMS,34(3),22. |
| MLA | Ji, Xia,et al."Direct sampling methods for inverse elastic scattering problems".INVERSE PROBLEMS 34.3(2018):22. |
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