Analysis of Electromagnetic Scattering from Penetrable Conductive Objects with IBC
Analysis of Electromagnetic Scattering from Penetrable Conductive Objects with IBC
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发表时间：
2015
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通讯作者：
Ping Li;Yifei Shi;L. J. Jiang;H. Bağcı
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作者：
Ping Li;Yifei Shi;L. J. Jiang;H. Bağcı
为了避免直接的体积离散，本文提出了一种结合阻抗边界条件（IBC）的间断Galerkin时域（DGTD）方法来分析有限电导率目标的电磁散射。考虑两种情况：i）趋肤深度小于导电体积的厚度; ii）趋肤深度大于薄导电片的厚度。对于第一种情况，采用表面阻抗边界条件（SIBC），其中表面阻抗通常表现出与频率的复杂关系。为了将SIBC纳入DGTD，表面阻抗首先使用快速松弛矢量拟合（FRVF）技术在拉普拉斯域中用有理函数近似。通过拉普拉斯逆变换，可以方便地得到时域DGTD矩阵方程关于时间t的积分形式。对于第二种情况，使用透射IBC（TIBC）来包括场的透明效果。在TIBC中，切向磁场跳跃通过表面电导率与切向电场有关。在这项工作中，开发了一种专门设计的带有TIBC的DGTD算法，以对太赫兹（THz）波段的石墨烯进行建模。为了将TIBC并入DGTD中而不涉及时域卷积，在石墨烯上引入由一阶微分方程控制的辅助表面极化电流。对于开区散射问题，DGTD算法进一步与时域边界积分（TDBI）方法杂交，严格截断计算区域。为了证明所提出的算法的准确性和适用性，提供了几个有代表性的例子。
To avoid straightforward volumetric discretization, a discontinuous Galerkin time-domain (DGTD) method integrated with the impedance boundary condition (IBC) is presented in this paper to analyze the scattering from objects with finite conductivity. Two situations are considered: i) the skin depth is smaller than the thickness of the conductive volume; ii) the skin depth is larger than the thickness of a thin conductive sheet. For the first situation, a surface impedance boundary condition (SIBC) is employed, wherein the surface impedance usually exhibits a complex relation with the frequency. To incorporate the SIBC into DGTD, the surface impedance is firstly approximated by rational functions in the Laplace domain using the fast relaxation vector-fitting (FRVF) technique. Via inverse Laplace transform, the time-domain DGTD matrix equations can be obtained conveniently in integral form with respect to time t. For the second situation, a transmission IBC (TIBC) is used to include the transparent effects of the fields. In the TIBC, the tangential magnetic field jump is related with the tangential electric field via the surface conductivity. In this work, a specifically designed DGTD algorithm with TIBC is developed to model the graphene up to the terahertz (THz) band. In order to incorporate the TIBC into DGTD without involving the time-domain convolution, an auxiliary surface polarization current governed by a first order differential equation is introduced over the graphene. For open-region scattering problems, the DGTD algorithm is further hybridized with the time-domain boundary integral (TDBI) method to rigorously truncate the computational domain. To demonstrate the accuracy and applicability of the proposed algorithm, several representative examples are provided.