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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DOI：
10.4208/csiam-am.2020-0013
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发表时间：
2020-04
期刊：
影响因子：
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通讯作者：
Xiaokai Yuan;Gang Bao;Peijun Li
中科院分区：
文献类型：
--
作者：
Xiaokai Yuan;Gang Bao;Peijun Li
考虑时谐电磁平面波对埋在无限大理想导电地平面中的开口空腔的散射。本文研究了横向极化和横向极化下开腔散射问题的数值解。基于Dirichlet-to-Neumann（DtN）映射，通过引入透明边界条件，将散射问题等价地转化为有界域上的边值问题.提出了一种基于后验误差估计的自适应有限元DtN方法。该估计由有限元逼近误差和截断误差的DtN算子，这是指数衰减的截断参数。两种偏振的数值实验来说明自适应方法的竞争行为。
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.