Multiple-Frequency Preconditioned Iterative Inverse Source Solutions

Abstract

Inverse source formulations relate unknown equivalent radiation sources to given field observations, which are commonly obtained from measurements. After discretization, the linear operator equation is advantageously solved in the form of an appropriate positive semidefinite normal system of equations. Several preconditioning strategies for the iterative solution of such linear systems of equations are investigated in this article. Observation point density-based preconditioners balance the effect of the constraint equations and speed up the solution process for globally irregular sample location distributions. Reduced-accuracy approximations of the radiation operator based on propagating plane-wave expansions of the pertinent Green’s functions can speed up the operator evaluation considerably. They are used within inner–outer iterative solvers or, even more efficiently, within a two-step iterative solution of the inverse source problem. Multiple-frequency inverse source solutions are considerably accelerated by start vector estimations from already available solutions for other nearby frequencies, where in particular a modified Galerkin approach is found to be very effective. The presented accelerated iterative solution approaches achieve the same accuracy levels as its not accelerated counterparts. They are validated and evaluated for a variety of near-field (NF) and far-field (FF) observation data of different antennas, whereby the benefits of the introduced solution approaches are of particular importance for large antennas with many unknowns.