  A Discontinuous Galerkin (DG) Finite Element Method (FEM) approach for the 3D
time dependent Maxwell equations in unbounded domains is presented. The method
(implemented in the FEM library NGsolve) is based on the covariant
transformation of a modal orthogonal polynomial basis, originally defined on a
reference simplex. The approach leads to an explicit time stepping scheme for
which the mass matrix to be inverted is at most $d\!\times\!d$ block-diagonal
(in $d\!=\!2,3$ spatial dimensions) while the matrix which discretizes the curl
operators on the right-hand side of the system is a small reference matrix,
independent from geometric properties of mesh elements. Furthermore, we show
that the introduced optimizations are preserved when unbounded domains are also
included in the formulation through a complex-stretching based approach.
