The factorization method for a penetrable cavity scattering with interior near-field measurements-Reference-Cited by-同舟云学术

The factorization method for a penetrable cavity scattering with interior near-field measurements

Published:2023-01-27 Issue:0 Volume:0 Page:
ISSN:0928-0219
Container-title:Journal of Inverse and Ill-posed Problems
language:en
Short-container-title:

Author:

Wu Qinghua¹,Guo Jun²,Yan Guozheng³^ORCID

Affiliation:

1. School of Mathematics and Statistics , Hubei Engineering University , Xiaogan , P. R. China

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

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

Abstract

Abstract This paper is concerned with the inverse scattering problem of time-harmonic acoustic waves from a penetrable cavity bounded by a layered structure and seeks to determine the shape and location of the cavity from interior near-field measurements. Of particular interest is that the near-field operator does not satisfy the main theorem of the factorization method, so we introduce a modified near-field operator and prove that it can be used to reconstruct the cavity. Numerical examples demonstrate the feasibility and effectiveness of our algorithm.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/jiip-2018-0111/pdf

Reference19 articles.

1. T. Angell and R. Kleinmann, The Helmholtz equation with L 2 {L^{2}} – boundary values, SIAM J. Math. Anal. 16 (1985), 259–278.

2. T. Angell and A. Kirsch, Optimization Methods in Electromagnetic Radiation, Springer, New York, 2004.

3. Y. Boukari and H. Haddar, The factorization method applied to cracks with impedance boundary conditions, Inverse Probl. Imaging 7 (2013), 1123–1138.

4. F. Cakoni and D. Colton, The linear sampling method for cracks, Inverse Problems 19 (2003), 279–295.

5. F. Cakoni, D. Colton and S. Meng, The inverse scattering problem for a penetrable cavity with internal measurements, Inverse Problems and Applications, Contemp. Math. 615, American Mathematical Society, Providence (2014), 71–88.