High-order contrast source inversion of dielectric targets using a Discontinuous Galerkin discretization of the vector wave equation

Abstract

The Finite-Element Method Contrast Source Inversion (FEM-CSI) algorithm is a versatile tool for solving electromagnetic imaging problems. Among the benefits of FEM-CSI are its ability to handle imaging system boundaries and inhomogeneous background media without requiring a numerical Green's function. Our more recent work has focused on extending the forward solver used in CSI to high-order by replacing the FEM formulation with a time-harmonic Discontinuous Galerkin Method (DGM) discretization of Maxwell's curl equations. Due to its high-order capabilities, DGM-CSI effectively decouples the contrast and field discretizations without introducing a dual mesh. The drawback of DGM-CSI based on Maxwell's curl equations is that it requires solving for both the electric and magnetic fields simultaneously, even when magnetic fields are not available in the measurement data. In this work we present CSI that uses a DGM discretization of the electric vector wave equation (VWE-DGM-CSI). This approach requires less time and memory than its counterpart based on the curl equations. If measurement data includes magnetic fields, the high-order electric field solution can be converted to magnetic fields using differential operators.