On a Frequency-Stabilized Single Current Inverse Source Formulation

TL;DR

This paper introduces a new inverse source formulation in electromagnetics that simplifies the process by solving for only one current, leading to computational savings and improved stabilization.

Contribution

The work presents a dual-element discretization and stabilization method for inverse source problems that retrieves Love data using a single current, enhancing efficiency and stability.

Findings

Effective quasi-Helmholtz projector stabilization demonstrated

Numerical tests confirm the method's efficiency and accuracy

Substantial computational savings achieved by solving for one current

Abstract

Several strategies are available for solving the inverse source problem in electromagnetics. Among them, many have been focusing in retrieving Love currents by solving, after regularization, for Love's electric and magnetic currents. In this work we present a dual-element discretization, analysis, and stabilization of an inverse source formulation providing Love data by solving for only one current. This results in substantial savings and allows for an effective quasi-Helmholtz projector stabilization of the resulting operator. Theoretical considerations are complemented by numerical tests showing effectiveness and efficiency of the newly proposed method.