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

When discontinuous Galerkin time-domain (DGTD) methods with explicit Runge-Kutta (RK) schemes are applied to the analysis of electromagnetic (EM) problems involving lossy media, the solution is highly unstable and the time-step size is more strictly restricted. To overcome this bottleneck, a novel implicit-explicit RK (IMEX RK) time-marching method is proposed for DGTD methods, using the implicit RK scheme for the conduction current term, while the explicit RK scheme for the rest. Numerical results demonstrate that the IMEX RK method can eliminate the numerical instability caused by lossy media compared with the explicit RK method and preserve high-order accuracy. In addition, to conquer the problem of exceedingly long execution time under low frequency and high resolution, the IMEX RK method is used for lossy regions, and a material scaling technique is used to enlarge the time-step size. For lossless regions, an unconditionally stable implicit time integration method is adopted to synchronize with lossy regions. The numerical results indicate that the proposed scheme is highly effective for solving low-frequency problems.