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A SPICE lumped circuit subcell model is formulated within the discontinuous Galerkin finite-element time-domain (DGFETD) discretization of Maxwell's equations. A fourth-order exponential time difference (ETD) algorithm is used for circuits that lead to stiff systems. The ETD method reduces to a standard fourth-order Runge-Kutta (RK4) time-integration for nonstiff regions. A number of test cases, including a microstrip transmission line terminated with general RLC networks, load arrays, and a diode detector are presented for the validation of the proposed hybrid DGFETD/SPICE solution method.