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A discontinuous Galerkin finite-element time-domain method is presented. The method is based on a high-order finite element discretization of Maxwell's time-dependent curl equations. The global volume is decomposed into contiguous sub-domains of finite-elements with independent function expansions. The fields are coupled across sub-domain boundaries by enforcing the tangential field continuity. This leads to a locally implicit, globally explicit difference operator that provides an efficient high-order accurate time-dependent solution.