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A highly parallel implementation of Maxwell's equations in the time domain using a cluster of Graphics Processing Units (GPUs) is presented. The higher-order Discontinuous Galerkin Finite Element Method (DG-FEM) is used for spatial discretization since its characteristics are matching the parallelization design aspects of the NVIDIA Compute Unified Device Architecture (CUDA) programming model. Asynchronous data transfer is introduced to minimize parallelization overhead and improve parallel efficiency. The implementation is benchmarked with help of a realistic 3-D geometry of an electromagnetic compatibility problem.