The discontinuous Galerkin finite element time-domain (DGFETD) method has been successfully applied to the solution of the coupled curl Maxwell’s equations. In this dissertation, important extensions to the DGFETD method are provided, including the ability to model lumped circuit elements and the ability to model thin-wire structures within a discrete DGFETD solution. To this end, a hybrid DGFETD/SPICE formulation is proposed for high-frequency circuit simulation, and a hybrid DGFETD/Thin-wire formulation is proposed for modeling thin-wire structures within a three-dimensional problem space. To aid in the efficient modeling of open-region structures, a Complex Frequency Shifted-Perfectly Matched Layer (CFS-PML) absorbing medium is applied to the DGFETD method for the first time. An efficient CFS-PML method that reduces the computational complexity and improves accuracy as compared to previous PML formulations is proposed. The methods have been successfully implemented, and a number of test cases are provided that validate the proposed methods. The proposed hybrid formulations and the new CFS-PML formulation dramatically enhances the ability of the DGFETD method to be efficiently applied to simulate complex, state of the art radio frequency systems.