Volume 4, Issue 3
Analysis of Direct and Inverse Cavity Scattering Problems

Gang Bao, Jinglu Gao & Peijun Li

Numer. Math. Theor. Meth. Appl., 4 (2011), pp. 335-358.

Published online: 2011-04

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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

Electromagnetic cavity, direct problem, inverse problem, finite element methods, boundary integral equations.

  • AMS Subject Headings

78A46, 78M30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-4-335, author = {}, title = {Analysis of Direct and Inverse Cavity Scattering Problems}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2011}, volume = {4}, number = {3}, pages = {335--358}, 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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2011.m1021}, url = {http://global-sci.org/intro/article_detail/nmtma/5972.html} }
TY - JOUR T1 - Analysis of Direct and Inverse Cavity Scattering Problems JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 335 EP - 358 PY - 2011 DA - 2011/04 SN - 4 DO - http://doi.org/10.4208/nmtma.2011.m1021 UR - https://global-sci.org/intro/article_detail/nmtma/5972.html KW - Electromagnetic cavity, direct problem, inverse problem, finite element methods, boundary integral equations. AB -

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.

Gang Bao, Jinglu Gao & Peijun Li. (2020). Analysis of Direct and Inverse Cavity Scattering Problems. Numerical Mathematics: Theory, Methods and Applications. 4 (3). 335-358. doi:10.4208/nmtma.2011.m1021
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