The Discontinuous Galerkin Finite-Element TimeDomain method is presented. The method is based on a highorder finite element discretization of Maxwell's time-dependent curl equations. The mesh is decomposed into contiguous subdomains of finite-elements with independent function expansions. The fields are coupled across the 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.An efficient implementation of the perfectly matched layer media boundary truncation is also presented that allows general tetrahedral meshing through the PML region.

A method is proposed for solving the time-dependent Maxwell's equations via the discontinuous Galerkin finite-element time-domain (DGFETD) method with dispersive media. An auxiliary differential equation (ADE) method is used to represent the constitutive relations. The method is applied to Drude materials, as well as to multiple pole Debye and Lorentz materials. An efficient implementation for high-order Runge-Kutta time integration schemes is presented. The method is validated and is shown to exhibit high-order convergence.Index Terms-Discontinuous Galerkin methods, electromagnetic propagation in dispersive media, finite element time-domain, high-order methods.

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