An explicit hybridizable discontinuous Galerkin method for the 3D time-domain Maxwell equations

We present an explicit hybridizable discontinuous Galerkin (HDG) method for numerically solving the system of three-dimensional (3D) time-domain Maxwell equations. The method is fully explicit similarly to classical so-called DGTD (Discontinuous Galerkin Time-Domain) methods that have been extensively studied during the last 15 years for the simulation of time-domain electromagnetic wave propagation. This HDGTD (Hybridizable Discontinuous Galerkin Time-Domain) method is also high-order accurate in both space and time and can be seen as a generalization of the classical DGTD scheme based on upwind fluxes. In particular, it coincides with the latter scheme for a particular choice of the stabilization parameter introduced in the definition of numerical traces in the HDG framework. It posseses a superconvergence property that allows, by means of local postprocessing, to obtain new improved approximations of the variables at any time levels. In particular, the new approximation converge with order k + 1 instead of k in the H curl-norm for k ≥ 1 .The proposed method has been implemented for dealing with general 3D problems. We provide numerical results aiming at assessing its numerical convergence properties by considering first a model problem. Then, this HDGTD method is applied to a classical scattering problem