Volume 1, Issue 2
An Adaptive Finite Element DtN Method for the Open Cavity Scattering Problems

Xiaokai Yuan, Gang Bao & Peijun Li

CSIAM Trans. Appl. Math., 1 (2020), pp. 316-345.

Published online: 2020-07

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  • 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.

  • Keywords

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

  • AMS Subject Headings

65M30, 78A45, 35Q60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CSIAM-AM-1-316, author = {Xiaokai Yuan , and Gang Bao , and Peijun Li , }, title = {An Adaptive Finite Element DtN Method for the Open Cavity Scattering Problems}, journal = {CSIAM Transactions on Applied Mathematics}, year = {2020}, volume = {1}, number = {2}, pages = {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.

}, issn = {2708-0579}, doi = {https://doi.org/10.4208/csiam-am.2020-0013}, url = {http://global-sci.org/intro/article_detail/csiam-am/17181.html} }
TY - JOUR T1 - An Adaptive Finite Element DtN Method for the Open Cavity Scattering Problems AU - Xiaokai Yuan , AU - Gang Bao , AU - Peijun Li , JO - CSIAM Transactions on Applied Mathematics VL - 2 SP - 316 EP - 345 PY - 2020 DA - 2020/07 SN - 1 DO - http://doi.org/10.4208/csiam-am.2020-0013 UR - https://global-sci.org/intro/article_detail/csiam-am/17181.html KW - Electromagnetic cavity scattering, TM and TE polarizations, adaptive finite element method, transparent boundary condition, a posteriori error estimates. AB -

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.

Xiaokai Yuan, Gang Bao & Peijun Li. (2020). An Adaptive Finite Element DtN Method for the Open Cavity Scattering Problems. CSIAM Transactions on Applied Mathematics. 1 (2). 316-345. doi:10.4208/csiam-am.2020-0013
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