An Explicit Nodal Space-Time Discontinuous Galerkin Method for Maxwell's Equations

A novel implicit nodal space-time discontinuous Galerkin (STDG) method is proposed in this letter. An eigenvalue analysis is performed and compared with that for a DG scheme solved with a fourth-order Runge-Kutta time integrator. We show that STDG offers a significant improvement of dissipative and dispersive properties and allows larger time steps, regardless of the spatial hp-refinement. A domain-decomposition technique is used to introduce an explicit formulation of the method in order to render it computationally efficient.