The Time-Domain Cell Method Is a Coupling of Two Explicit Discontinuous Galerkin Schemes with Continuous Fluxes

The cell method (CM) or discrete geometric approach (DGA) in the time domain, already introduced by Codecasa et al. in 2008 for the coupled Ampere-Maxwell and Faraday equations, is here recast as a Galerkin Method similar to the finite-element method (FEM). In particular, it is shown to be a mixed method comprising an explicit scheme and two discontinuous Galerkin (DG) FEM spaces formulated on dual meshes, in which each of the two function spaces provides a continuous numerical flux choice for its dual mesh counterpart. The implemented version is shown to compare favorably in terms of accuracy and efficiency with respect to the classic conforming FEM scheme using Whitney elements. When tested on the same tetrahedral mesh, the Courant-Friedrichs-Lewy (CFL) condition for the proposed approach is a factor of 2 less restrictive on the time step with respect to the curl-conforming FEM scheme.