The factorization and monotonicity method for the defect in an open periodic waveguide

Author:

Furuya Takashi1ORCID

Affiliation:

1. Graduate School of Mathematics , Nagoya University , Furocho, Chikusa-ku , Nagoya 464-8602 , Japan

Abstract

Abstract We consider the inverse scattering problem to reconstruct the defect in an infinite medium with periodicity in the upper half space from near field data. This paper has two contributions. Firstly, we mention that there is a mistake in the factorization method of the earlier paper [A. Lechleiter, The factorization method is independent of transmission eigenvalues, Inverse Probl. Imaging 3 2009, 1, 123–138] and give the correct one. Secondly, we give two reconstruction algorithms for the unknown defect by a combination of the factorization method and the monotonicity method. We also give numerical examples based on the former algorithm.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics

Reference26 articles.

1. K. A. Anagnostopoulos, A. Charalambopoulos and A. Kleefeld, The factorization method for the acoustic transmission problem, Inverse Problems 29 (2013), no. 11, Article ID 115015.

2. O. Bondarenko, A. Kirsch and X. Liu, The factorization method for inverse acoustic scattering in a layered medium, Inverse Problems 29 (2013), no. 4, Article ID 045010.

3. A.-S. Bonnet-Ben Dhia, G. Dakhia, C. Hazard and L. Chorfi, Diffraction by a defect in an open waveguide: A mathematical analysis based on a modal radiation condition, SIAM J. Appl. Math. 70 (2009), no. 3, 677–693.

4. L. Bourgeois and S. Fliss, On the identification of defects in a periodic waveguide from far field data, Inverse Problems 30 (2014), no. 9, Article ID 095004.

5. S. N. Chandler-Wilde and B. Zhang, Electromagnetic scattering by an inhomogeneous conducting or dielectric layer on a perfectly conducting plate, R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 454 (1998), no. 1970, 519–542.

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