The marching-on-in-degree (MOD) method is applied in this paper to analyze the transient electromagnetic scattering of multilayer graphene and a dielectric substrate. The time domain resistive boundary condition (TD-RBC) integral equation and time domain Poggio–Miller–Chang–Harrington–Wu (PMCHW) integral equation of electric and magnetic currents are employed to model graphene and the dielectric substrate, respectively. These two sets of equations are coupled and solved with the MOD method. The dispersion of multilayer graphene’s surface conductivity/resistivity in the frequency domain is taken into account in the analytical convolution of temporal surface conductivity/resistivity and magnetic/electric current densities. The Rao-Wilton-Glisson (RWG) basis function over triangle patches and weighted Laguerre polynomial (WLP) are used as the spatial and temporal basis/testing functions, respectively. The orthogonal WLPs are defined from zero to +∞ and are convergent to zero with time passing. These advantages ensure late time stability of the transient solution. A stable electric/magnetic current is achieved. A radar cross section and extinction cross section in the frequency domain are also obtained and compared with commercial software results to verify the proposed method.

中文翻译：

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逐行进度法分析带电介质的多层石墨烯的瞬态电磁分析

本文采用渐进式（MOD）方法来分析多层石墨烯和介电基体的瞬态电磁散射。电流和磁电流的时域电阻性边界条件（TD-RBC）积分方程和Poggio-Miller-Chang-Harrington-Wu（PMCHW）时域积分方程分别用于建模石墨烯和介电基板。这两组方程式通过MOD方法耦合并求解。在时间表面电导率/电阻率和磁/电流密度的分析卷积中考虑了多层石墨烯的表面电导率/电阻率在频域中的分散。三角形面片上的Rao-Wilton-Glisson（RWG）基础函数和加权Laguerre多项式（WLP）分别用作空间和时间基础/测试函数。正交WLP定义为从零到+∞，并且随着时间的流逝收敛到零。这些优势确保了瞬态解决方案的后期稳定性。实现了稳定的电磁电流。还获得了频域中的雷达横截面和消光横截面，并将其与商业软件结果进行比较以验证所提出的方法。