The Discontinuous Galerkin time-domain method (DGTD) can be seen a finite element type method in which the continuity between elements has been released . This leads to very good properties (stencil compactness, possible local h-p adaptation) in view of dealing with complex wave-propagation problems in heterogeneous media [2, 3]. One of the fruits of the research conducted at the Nachos project-team on the formulation and implementation of
numerical methodologies based on the DGTD method is a parallel solver of 3D Maxwells equations on unstructured meshes which we refer to as MAXW-DGTD. In this talk, we will start by recalling the idea of the method. Then, we will give an overview of recent progress on the implementation, in MAXW-DGTD, of a hybrid coarse grain (MPI) / fine grain (OpenMp) parallelization strategy. One of the motivations behind this is to achieve good scalability results on the heterogeneous cluster/accelerator architecture proposed in the
DEEP-ER exascale european project, on which MAXW-DGTD is currently being adapted. Finally, we will also briefly discuss future plans of including MAXW-DGTD as a low-level solver embedded in the Multiscale Hybrid Method (MHM) framework developed at LNCC by Harder et al. .
 Fezoui, L., Lanteri, S., Lohrengel, S. and Piperno, S., Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes. ESAIM: Math. Model. Numer. Anal., Vol. 39, No. 6, pp. 11491176,
 Fahs, H., Hadjem, A., Lanteri, S., Wiart, J. and Wong, M.F., Calculation of the SAR induced in head tissues using a high order DGTD method and triangulated geometrical models. IEEE Trans. Ant. Propag., Vol. 59, No. 12, pp. 4669-4678, 2011.
 Léger, R., Viquerat, J., Durochat, C., Scheid, C. and Lanteri, S., A parallel non-conforming multi/element DGTD method for the simulation of electromagnetic wave interaction with metallic nanoparticles. Journal of Computational and Applied Mathematics, ISSN 0377-0427, http://dx.doi.org/10.1016/j.cam.2013.12.042.
 Harder, C., Paredes, D. and Valentin, F., A family of multiscale hybrid-mixed finite element methods for the Darcy equation with rough coefficients. Journal of Computation Physics, Vol. 245, pp. 107-130, 2013.