A Stable Discontinuous Galerkin Time-Domain Method for Simulation of Thin Conductive Layers

A conductive layer that is much thinner than the skin depth is often incorporated into electromagnetic solvers as a resistive boundary condition (RBC) to avoid fine meshes (and consequently small time steps for time-domain methods). When the discontinuous Galerkin time-domain (DGTD) method, which relies on an explicit Runge-Kutta (RK) scheme for time integration, is used in a simulation involving an RBC surface with high conductivity, the solution becomes unstable. In this work, to circumvent this bottleneck, a locally-implicit time marching scheme is developed. The proposed method uses implicit Euler backward and explicit Euler forward schemes to discretize the time derivatives in local DG equations associated with the elements that "touch" and do not "touch" the RBC surface, respectively. This yields a locally-implicit Euler (LIME) time marching scheme that maintains its stability in the presence of a highly conductive layer. Indeed, numerical results demonstrate that LIME-DGTD is more stable than RK-DGTD for a transmission problem involving a thin metal sheet.