A Stable Discontinuous Galerkin Time-Domain Method with Implicit-Explicit Time-Marching for Lossy Media

When the discontinuous Galerkin time-domain (DGTD) method with the explicit Runge-Kutta (RK) scheme is used to solve the electromagnetic problems involving lossy media, the solution is highly unstable and the time-step size is more strictly restricted. To overcome this bottleneck, we introduce the implicit-explicit RK (IMEX RK) method to the DGTD method, using the implicit RK scheme for the time marching of the conduction current term, while the explicit RK scheme for the rest, which can eliminate the instability caused by lossy media. Numerical results demonstrate that the proposed method breaks the limitation of the time-step size due to non-zero conductivity compared with the explicit RK method and preserves high-order accuracy.