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Analysis of Direct and Inverse Cavity Scattering Problems

Published online by Cambridge University Press:  28 May 2015

Gang Bao,
Jinglu Gao and
Peijun Li
Gang Bao*
Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou 310027, ChinaDepartment of Mathematics, Michigan State University, East Lansing, MI 48824, USA
Jinglu Gao*
Affiliation:
School of Mathematical Sciences, Jilin University, Changchun 130023, China
Peijun Li*
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA
*
Corresponding author.Email address:bao@math.msu.edu
Corresponding author.Email address:jinglugao@gmail.com
Corresponding author.Email address:lipeijun@math.purdue.edu
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Abstract

Consider the scattering of a time-harmonic electromagnetic plane wave by an arbitrarily shaped and filled cavity embedded in a perfect electrically conducting infinite ground plane. A method of symmetric coupling of finite element and boundary integral equations is presented for the solutions of electromagnetic scattering in both transverse electric and magnetic polarization cases. Given the incident field, the direct problem is to determine the field distribution from the known shape of the cavity; while the inverse problem is to determine the shape of the cavity from the measurement of the field on an artificial boundary enclosing the cavity. In this paper, both the direct and inverse scattering problems are discussed based on a symmetric coupling method. Variational formulations for the direct scattering problem are presented, existence and uniqueness of weak solutions are studied, and the domain derivatives of the field with respect to the cavity shape are derived. Uniqueness and local stability results are established in terms of the inverse problem.

Keywords

78A4678M30Electromagnetic cavitydirect probleminverse problemfinite element methodsboundary integral equations

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Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 4 , Issue 3 , August 2011, pp. 335 - 358
Copyright
Copyright © Global Science Press Limited 2011

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