Efficient electromagnetic analysis of multi‐layer and multi‐scale periodic/quasi‐periodic structures

Abstract

Abstract To increase the electromagnetic analysis efficiency, the fast and memory efficient discontinuous Galerkin time‐domain (DGTD) method, which can simulate expeditiously the multi‐scale and multi‐layer periodic/quasi‐periodic structures, is proposed in this study. For one thing, this method is highly targeted for multi‐layer quasi‐periodic structures. It realises that the quasi‐periodic structure is extended from one layer to multiple layers. At the same time, the unit cells of the structure are no longer the conventional square lattice, and the sizes of different types of unit cells cannot be required for the same. For another, the implicit–explicit Runge–Kutta (ImEx‐RK) time stepping scheme has been widely employed for time integration, which can break the limitation of the Courant–Friedrichs–Levy condition. However, the ImEx‐RK time stepping scheme had been an under‐explored domain in periodic/quasi‐periodic structures, so it was introduced into the memory efficient DGTD method to decrease the simulation time. That is, the electrically coarse and fine subdomains in the multiscale periodic/quasi‐periodic structures can be separated such that implicit schemes can be utilised in the fine subdomains. The correctness and advance of this method are proved by several classical numerical examples.

Keywords

• discontinuous Galerkin time‐domain method
• implicit‐explicit Runge‐Kutta time stepping scheme
• multi‐layer and multi‐scale periodic/quasi‐periodic structures