Inverse Fluid-solid Interaction Scattering Problem Using Phased and Phaseless Far Field Data
文献类型：期刊论文
| 作者 | Ji, Xia2 ; Jia, Yun-fei1,3; Liu, Xiao-dong1
|
| 刊名 | ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES
 |
| 出版日期 | 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 |
| WOS记录号 | WOS:000504613100006 |
| 出版者 | SPRINGER HEIDELBERG |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/50522]  |
| 专题 | 计算数学与科学工程计算研究所 应用数学研究所 |
| 通讯作者 | Liu, Xiao-dong |
| 作者单位 | 1.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
浏览0
下载0
收藏0
其他版本
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。