A 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 that 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. 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.