Direct sampling methods for inverse elastic scattering problems
文献类型：期刊论文
| 作者 | Ji, Xia1 ; Liu, Xiaodong2; Xi, Yingxia3
|
| 刊名 | INVERSE PROBLEMS
 |
| 出版日期 | 2018-03-01 |
| 卷号 | 34期号:3页码:22 |
| 关键词 | elastic scattering sampling method far field pattern limited-aperture problem |
| ISSN号 | 0266-5611 |
| DOI | 10.1088/1361-6420/aaa996 |
| 英文摘要 | 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. |
| 资助项目 | 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研究方向 | Mathematics ; Physics |
| 语种 | 英语 |
| WOS记录号 | WOS:000424903900001 |
| 出版者 | IOP PUBLISHING LTD |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/449]  |
| 专题 | 应用数学研究所 计算数学与科学工程计算研究所 |
| 通讯作者 | Ji, Xia |
| 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, Inst Appl Math, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Beijing 100190, Peoples R China |
| 推荐引用方式 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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