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An Adaptive Finite Element DtN Method for the Open Cavity Scattering Problems

An Adaptive Finite Element DtN Method for the Open Cavity Scattering Problems
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Year:    2020

Author:    Xiaokai Yuan, Gang Bao, Peijun Li

CSIAM Transactions on Applied Mathematics, Vol. 1 (2020), Iss. 2 : pp. 316–345

Abstract

Consider the scattering of a time-harmonic electromagnetic plane wave by an open cavity which is embedded in a perfectly electrically conducting infinite ground plane. This paper concerns the numerical solutions of the open cavity scattering problems in both transverse magnetic and transverse electric polarizations. Based on the Dirichlet-to-Neumann (DtN) map for each polarization, a transparent boundary condition is imposed to reduce the scattering problem equivalently into a boundary value problem in a bounded domain. An a posteriori error estimate based adaptive finite element DtN method is proposed. The estimate consists of the finite element approximation error and the truncation error of the DtN operator, which is shown to decay exponentially with respect to the truncation parameter. Numerical experiments are presented for both polarizations to illustrate the competitive behavior of the adaptive method.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/csiam-am.2020-0013

CSIAM Transactions on Applied Mathematics, Vol. 1 (2020), Iss. 2 : pp. 316–345

Published online:    2020-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    30

Keywords:    Electromagnetic cavity scattering TM and TE polarizations adaptive finite element method transparent boundary condition a posteriori error estimates.

Author Details

Xiaokai Yuan

Gang Bao

Peijun Li

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