The linear sampling method for penetrable cylinder with inclusions for obliquely incident polarized electromagnetic waves-Reference-Cited by-同舟云学术

The linear sampling method for penetrable cylinder with inclusions for obliquely incident polarized electromagnetic waves

Published:2022-03-31 Issue:3 Volume:30 Page:331-349
ISSN:0928-0219
Container-title:Journal of Inverse and Ill-posed Problems
language:en
Short-container-title:

Author:

Deng Xia¹,Guo Jun²,Li Jin³,Yan Guozheng⁴^ORCID

Affiliation:

1. School of Mathematics , Changsha Normal University , Changsha , 410100 , P. R. China

2. School of Mathematics and Statistics , South-Central University For Nationalities , Wuhan 430074 , P. R. China

3. School of Science , Guangdong University of Petrochemical Technology , Maoming 525000 , P. R. China

4. School of Mathematics and Statistics , Central China Normal University , Wuhan 430079 , P. R. China

Abstract

Abstract Consider the scattering of electromagnetic waves by a penetrable homogeneous cylinder at oblique incident. The Maxwell equations are then reduced to a system of a pair of the two-dimensional Helmholtz equations for 𝑧-components of the electric and magnetic field through coupled oblique boundary conditions. This paper studies an inverse problem of recovering the penetrable obstacle from the far-field pattern of the electric field. The well-known linear sampling method is used to solve this problem. Compared with the usual inverse scattering problem, the coupled system and the oblique derivative boundary condition bring difficulties in theoretical analysis. Some numerical examples are presented to illustrate the validity and feasibility of the proposed method.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/jiip-2019-0056/pdf

Reference21 articles.

1. M. Brühl and M. Hanke, Numerical implementation of two noniterative methods for locating inclusions by impedance tomography, Inverse Problems 16 (2000), no. 4, 1029–1042.

2. F. Cakoni and D. Colton, Qualitative Methods in Inverse Scattering Theory, Interact. Mech. Math., Springer, Berlin, 2006.

3. A. Charalambopoulos, D. Gintides and K. Kiriaki, The linear sampling method for non-absorbing penetrable elastic bodies, Inverse Problems 19 (2003), no. 3, 549–561.

4. Q. Chen, H. Haddar, A. Lechleiter and P. Monk, A sampling method for inverse scattering in the time domain, Inverse Problems 26 (2010), no. 8, Article ID 085001.

5. F. Collino, M. Fares and H. Haddar, Numerical and analytical studies of the linear sampling method in electromagnetic inverse scattering problems, Inverse Problems 19 (2003), no. 6, 1279–1298.