Interior Penalty Discontinuous Galerkin Method for the Time-Domain Maxwell's Equations

Discontinuous Galerkin (DG) methods support elements of various types, nonmatching grid and varying polynomial order in each element. In DG methods continuity at element interfaces is weakly enforced with the addition of proper penalty terms on the variational formulation commonly referred to as numerical fluxes. An interior penalty approach to derive a DG method for solving the two first order Maxwell's equations in the time domain is presented. The proposed method is explicit and conditionally stable. In addition, a local time-stepping strategy is applied to increase efficiency and reduce the computational time.