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A Discontinuous Galerkin (DG) Finite Element Method (FEM) approach for the 3Dtime dependent Maxwell equations in unbounded domains is presented. The method(implemented in the FEM library NGsolve) is based on the covarianttransformation of a modal orthogonal polynomial basis, originally defined on areference simplex. The approach leads to an explicit time stepping scheme forwhich 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 curloperators on the right-hand side of the system is a small reference matrix,independent from geometric properties of mesh elements. Furthermore, we showthat the introduced optimizations are preserved when unbounded domains are alsoincluded in the formulation through a complex-stretching based approach.

A matrix-free Discontinuous Galerkin method for the time dependent Maxwell equations in unbounded domains