Stabilized Single Current Inverse Source Formulations Based on Steklov-Poincar\'e Mappings

TL;DR

This paper introduces a novel, stable, reduced-size inverse source formulation in electromagnetics that leverages Steklov-Poincaré mappings and low-frequency stabilization, improving computational efficiency and robustness.

Contribution

It presents the first low-frequency stabilized inverse source formulation based on Steklov-Poincaré mappings, reducing system size and enhancing stability in electromagnetics applications.

Findings

Effective numerical results demonstrating stability and accuracy.

Theoretical validation of the low-frequency stabilization approach.

Reduced computational complexity compared to traditional methods.

Abstract

The inverse source problem in electromagnetics has proved quite relevant for a large class of applications. In antenna diagnostics in particular, Love solutions are often sought at the cost of an increase of the dimension of the linear system to be solved. In this work, instead, we present a reduced-in-size single current formulation of the inverse source problem that obtains one of the Love currents via a stable discretization of the Steklov-Poincar\'e boundary operator leveraging dual functions. The new approach is enriched by theoretical treatments and by a further low-frequency stabilization of the Steklov-Poincar\'e operator based on the quasi-Helmholtz projectors that is the first of its kind in this field. The effectiveness and practical relevance of the new schemes are demonstrated via both theoretical and numerical results.