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In this paper we present three-dimensional numerical simulations of electromagnetic waves. The Maxwell equations are solved by the Discontinuous Galerkin (DG) method. For achieving high performance, we exploit two levels of parallelism. The coarse grain parallelism is managed through MPI and a classical domain decomposition. The fine grain parallelism is managed with OpenCL in order to optimize the local computations on multicore processors or GPU’s. We present several numerical experiments and performance comparisons.