A Locally-Implicit Discontinuous Galerkin Time-Domain Method to Simulate Metasurfaces Using Generalized Sheet Transition Conditions

Abstract

The generalized sheet transition conditions (GSTCs) are incorporated into a discontinuous Galerkin time-domain (DGTD) method to efficiently simulate metasurfaces. The numerical flux for GSTCs is derived for the first time using the Rankine-Hugoniot jump conditions. This numerical flux includes time derivatives of fields and therefore explicit time integration schemes, which are traditionally used with DGTD, do not yield a stable time marching method. To alleviate this bottleneck, a new time marching scheme, which solves a local matrix system for the unknowns of the elements touching the same GSTC face, is developed. This locally-implicit method maintains its high-parallel efficiency just like the traditional explicit DGTD schemes. Numerical results, which validate the accuracy of the proposed method against analytical solutions and demonstrate its applicability to the simulation of curved and space/time-varying metasurfaces, are presented. Index Terms-discontinuous Galerkin time-domain method, finite element method, generalized sheet transition conditions, metasurface, numerical flux, time-domain analysis, time integration.