A Local Time-Stepping Discontinuous Galerkin Time-Domain Scheme for Simulation of Electromagnetic Problems Involving Resistive Boundary Condition

Thin layers with high conductivity values, such as metal sheets, conductive paint, graphene, and other two-dimensional (2D) materials, are commonly used in various electromagnetic applications. One of the fundamental challenges in numerical modeling of these thin conductive layers is the requirement for an extremely fine mesh that can accurately capture field variations and account for the intricate geometrical features of the structure (H. Chen, A. J. Taylor and N. Yu, Rep. Prog. Phy., 79,10-35,2016). A dense mesh translates into high computational cost since the number of unknowns is increased and the time step size must be reduced for an explicit time marching scheme (to ensure that the Courant-Friedrichs-Lewy (CFL) condition is satisfied). One can replace the thin conductive layer with an infinitesimally thin sheet on which the resistive boundary condition (RBC) is enforced (T. B. A. Senior and J. L. Volakis, London, UK: IET, 1995). This approach completely avoids the dense mesh and the high computational cost that comes with it. However, RBC has to be incorporated into the electromagnetic solver.