Construction of Discontinuous Galerkin Time Domain methods for Maxwell's equations on staggered grids

We propose a class of DG methods for the solution of Maxwell's equations in the time domain using staggered grid discretization. The method can be regarded as a generalization of the well-known FDTD technique. The present approach, however, applies to high order approximations as well. In terms of numerical properties, the method shares the energy conservation property with central flux DG formulations. On the other hand, the method is optimally convergent as is the case for dissipative DG methods using upwind fluxes. We perform a Bloch wave dispersion analysis in the one dimensional case. It shows that grid staggering allows to eliminate the spurious mode solutions originating from odd-even decoupling which are otherwise present in common DG formulations.