分析石墨烯瞬态电磁特性的时域积分方程方法研究

Graphene is the disruptive new material, which has been found applicable and promising in many fields, e.g. electromagnetic and communication systems. It is infinitely thin, dispersive, and difficult for accurate modeling and numerical simulation. Solving graphene involved transient problems at light frequencies, the efficiency of conventional frequency domain methods decreases. This project aims at developing a fast numerical solver for transient responses of graphene on the dielectric substrate, based on time domain integral equations. Time domain surface impedance of graphene is obtained, and time domain integral equation is established with surface impedance boundary condition. Usage of weighted Laguerre polynomials as temporal bases ensures stable solution even in late time. The derivative and integration of time domain current with respect to time t, and the convolution of time domain current and surface impedance are deduced analytically. As for graphene patches on the dielectric substrate, time domain PMCHWT formulation are involved. Fast algorithm is utilized to reduce computation complexity in the marching-on-in-degree scheme. The research is of great significance in both theory and application. Simulation and design of graphene based electromagnetic and communication devices will be stimulated.

石墨烯作为新材料在电磁、通信系统等多个领域具有重要应用前景。它无限薄，表现出色散特性，精确建模与数值分析复杂。研究石墨烯在光频的瞬态电磁特性时，传统的频域方法效率降低。本项目针对石墨烯器件的应用需求与数值分析的发展需要，基于时域积分方程，建立计算含衬底的石墨烯结构瞬态响应的数值方法。获得石墨烯的时域表面阻抗，通过时域表面阻抗边界条件建立时域积分方程。以加权Laguerre多项式作为时间基函数，推导石墨烯表面时域电流对时间求导、积分、与时域表面阻抗卷积的解析公式，进行阶数步进求解，获得晚时无条件稳定的瞬态结果。当石墨烯含有衬底时，结合稳定、准确的时域PMCHWT方程进行求解。阶数步进求解计算资源耗费巨大，为此引入快速方法进行加速。项目极具科学理论意义和工程应用价值，将推进石墨烯电磁与通信器件的仿真与设计。

石墨烯一种具有重要应用前景的新材料。它只有若干碳原子厚，具有色散特性，精确建模与数值分析复杂。研究石墨烯的瞬态电磁特性时，传统的频域方法效率较低。本项目针对应用需求，建立分析含介质衬底的石墨烯结构瞬态响应的时域积分方程方法。构造和使用高层级基函数，极大减少了阶数步进时域积分方程方法的矩阵存储和内存需求。采用矢量匹配法，用若干项极点和留数展开石墨烯频域表面阻抗，再经逆傅里叶变换到时域，获得石墨烯的时域表面阻抗，并获得了多层石墨烯的表面电导率与阻抗。通过时域表面阻抗边界条件，结合PMCHW方程，建立时域积分方程。以加权Laguerre多项式作为时间基函数，推导了石墨烯表面时域电流/磁流与时域表面阻抗/电导率卷积的解析公式，进行阶数步进求解，获得了晚时无条件稳定的瞬态结果。项目极具科学理论意义和工程应用价值，将推进石墨烯电磁与通信器件的仿真与设计。