Formulation of the Hardy space method in a Discontinuous Galerkin framework

Local transparent boundary conditions (TBCs) based upon the pole condition have shown a great deal of promise in recent years. Only recently has the pole condition been applied to the Maxwell Equations with the aid of vector Hardy space infinite elements [1]. In this work, we describe a variation on the conformal Finite Element formulation presented in [1] within an interior penalty Discontinuous Galerkin (DG) framework. Our primary reasons for doing so are the use of nonconformal meshing at the interior/exterior boundary and the use of locally-enriched function spaces to include desirable physics in numerical solutions.