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

—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.