In this paper, we consider the electromagnetic concentrator model obtained through transformation optics. This model is formed by a system of coupled time-dependent Maxwell’s equations with three unknowns, which makes the analysis and simulation much more challenging compared to the standard Maxwell equations. In our previous work (W. Yang, J. Li, Y. Huang, and B. He, Commun. Comput. Phys., 25(1), pp. 135–154, 2019), we proposed a finite element time-domain (FETD) method with edge elements for solving this model efficiently without any theoretical analysis. Here, we provide a rigorous analysis for the mathematical modelling equations and the FETD method proposed there.

在本文中，我们考虑了通过转换光学获得的电磁集中器模型。该模型由具有三个未知数的耦合时间相关的麦克斯韦方程组组成，与标准麦克斯韦方程相比，分析和模拟更具挑战性。在我们以前的工作中（W. Yang，J。Li，Y。Huang，和B. He，Commun。Comput。Phys。，25（1），第135-154页，2019年），我们提出了一个有限元时间-边缘元素的有限域（FETD）方法无需任何理论分析即可有效地求解此模型。在这里，我们对其中提出的数学建模方程和FETD方法进行了严格的分析。