Stabilized Single Current Inverse Source Formulations Based on Steklov-Poincaré Mappings

The inverse source problem in electromagnetics has proved quite relevant for a large class of applications. When it is coupled with the equivalence theorem, the sources are often evaluated as electric and/or magnetic current distributions on an appropriately chosen equivalent surface. In this context, in antenna diagnostics in particular, Love solutions, i.e., solutions which radiate zero-fields inside the equivalent surface, 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-Poincaré boundary operator leveraging dual functions. The new approach is enriched by theoretical treatments and by a further low-frequency stabilization of the Steklov-Poincaré 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