A Mixed Discontinuous Galerkin Formulation for Time-Harmonic Scattering Problems

The time-harmonic Discontinuous Galerkin Method (DGM) is a flexible forward solver for inverse scattering problems in electromagnetics. Standard DGM discretizations of Maxwell's curl equations, simultaneously solving for both electric and magnetic fields, are generally more accurate but less efficient than the DGM applied to the electric vector wave equation. A natural extension is to mix DGM formulations such that either the curl equation formulation or the wave equation formulation is locally adopted to preserve accuracy. Herein we present such a mixed DGM formulation for time-harmonic scattering problems, where the formulation choice is locally based on the presence of electric or magnetic constitutive parameters that differ from the background medium.