Stability Analysis of Discontinuous Galerkin Time-Domain Method for Conductive Media

In this study, the effect of conductivity on the stability of the discontinuous Galerkin time-domain (DGTD) method, which uses Runge-Kutta (RK) or leap-frog (LF) (time-averaging, time-forward, and time-backward) schemes to integrate the Maxwell equations in time, is studied. As a test case, transient reflection from one-dimensional conductive half-space, for which the analytical solution exists, is considered. Numerical results demonstrate that the LF-DGTD schemes, which use time-averaging and time-forward, are significantly more stable and faster than the RK-DGTD scheme for problems involving conductive materials.