KMS Of Academy of mathematics and systems sciences, CAS
| A NOVEL INTEGRAL EQUATION FOR SCATTERING BY LOCALLY ROUGH SURFACES AND APPLICATION TO THE INVERSE PROBLEM: THE NEUMANN CASE | |
Qu, Fenglong1; Zhang, Bo2,3,4 ; Zhang, Haiwen3,5,6
| |
| 2019 | |
| Source Publication | SIAM JOURNAL ON SCIENTIFIC COMPUTING
 |
| ISSN | 1064-8275 |
| Volume | 41Issue:6Pages:A3673-A3702 |
| Abstract | This paper is concerned with direct and inverse scattering by a locally perturbed infinite plane (called a locally rough surface in this paper) on which a Neumann boundary condition is imposed. A novel integral equation formulation is proposed for the direct scattering problem which is defined on a bounded curve (consisting of a bounded part of the infinite plane containing the local perturbation and the lower part of a circle) with two corners and some closed smooth artificial curve. It is a nontrivial extension of our previous work on direct and inverse scattering by a locally rough surface from the Dirichlet boundary condition to the Neumann boundary condition [SIAM T. Appl. Math., 73 (2013), pp. 1811-1829]. For the Dirichlet boundary condition, the integral equation obtained is uniquely solvable in the space of bounded continuous functions on the bounded curve, and it can be solved efficiently by using the Nystrom method with a graded mesh. However, the Neumann condition case leads to an integral equation which is solvable in the space of squarely integrable functions on the bounded curve rather than in the space of bounded continuous functions, making the integral equation very difficult to solve numerically with the classic and efficient Nystrom method. In this paper, we make use of the recursively compressed inverse preconditioning method developed by Helsing to solve the integral equation which is efficient and capable of dealing with large wave numbers. For the inverse problem, it is proved that the locally rough surface is uniquely determined from a knowledge of the far-field pattern corresponding to incident plane waves. Moreover, based on the novel integral equation formulation, a Newton iteration method is developed to reconstruct the locally rough surface from a knowledge of multiple frequency far-field data. Numerical examples are also provided to illustrate that the reconstruction algorithm is stable and accurate even for the case of multiple-scale profiles. |
| Keyword | integral equation locally rough surface Neumann boundary condition far-field pattern RCIP method Newton iteration method |
| DOI | 10.1137/19M1240745 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | NNSF of China[11871416] ; NNSF of China[11871466] ; NNSF of China[91630309] ; Shandong Provincial Natural Science Foundation[ZR2019MA027] ; Shandong Provincial Natural Science Foundation[ZR2017MA044] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000549131500019 |
| Publisher | SIAM PUBLICATIONS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/51817 |
| Collection | 应用数学研究所 |
| Corresponding Author | Zhang, Haiwen |
| Affiliation | 1.Yantai Univ, Sch Math & Informat Sci, Yantai 264005, Shandong, Peoples R China 2.Chinese Acad Sci, NCMIS, LSEC, Beijing 100190, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 5.Chinese Acad Sci, NCMIS, Beijing 100190, Peoples R China 6.Univ Gottingen, Inst Numer & Appl Math, Lotzestr 16-18, D-37083 Gottingen, Germany |
| Recommended Citation GB/T 7714 | Qu, Fenglong,Zhang, Bo,Zhang, Haiwen. A NOVEL INTEGRAL EQUATION FOR SCATTERING BY LOCALLY ROUGH SURFACES AND APPLICATION TO THE INVERSE PROBLEM: THE NEUMANN CASE[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2019,41(6):A3673-A3702. |
| APA | Qu, Fenglong,Zhang, Bo,&Zhang, Haiwen.(2019).A NOVEL INTEGRAL EQUATION FOR SCATTERING BY LOCALLY ROUGH SURFACES AND APPLICATION TO THE INVERSE PROBLEM: THE NEUMANN CASE.SIAM JOURNAL ON SCIENTIFIC COMPUTING,41(6),A3673-A3702. |
| MLA | Qu, Fenglong,et al."A NOVEL INTEGRAL EQUATION FOR SCATTERING BY LOCALLY ROUGH SURFACES AND APPLICATION TO THE INVERSE PROBLEM: THE NEUMANN CASE".SIAM JOURNAL ON SCIENTIFIC COMPUTING 41.6(2019):A3673-A3702. |
| Files in This Item: | There are no files associated with this item. | |||||
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.
Edit Comment