Discontinuous Galerkin Time Domain Modeling of Metasurface Geometries with Multi-rate Time Stepping

We present a time-domain modeling framework for electromagnetic metasurfaces based on the Discontinuous Galerkin Time Domain (DGTD) method. In particular, we employ the unstructured mesh and the inherent $h$ - $p$ refinement ability of DGTD to efficiently model multiscale geometries via adaptive mesh refinement. More importantly, the cost of mesh refinement is alleviated by the implementation of multi-rate time stepping in a stable fashion. Our approach addresses major challenges associated with current and emerging trends in the design of metasurfaces, an area of microwave engineering with significant potential.