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The accurate solution of quasi-Helmholtz decomposed electric field integral equations (EFIEs) in the presence of arbitrary excitations is addressed: Depending on the specific excitation, the quasi-Helmholtz components of the induced current density do not have the same asymptotic scaling in frequency, and thus, the current components are solved for with, in general, different relative accuracies. In order to ensure the same asymptotic scaling, we propose a frequency normalization scheme of quasi-Helmholtz decomposed EFIEs which adapts itself to the excitation and which is valid irrespective of the specific excitation and irrespective of the underlying topology of the structure. Specifically, neither an ad-hoc adaption nor a-priori information about the excitation is needed as the scaling factors are derived based on the norms of the right-hand side (RHS) components and the frequency. Numerical results corroborate the presented theory and show the effectiveness of our approach.

The electric field integral equation (EFIE) is known to suffer from ill-conditioning and numerical instabilities at low frequencies (low-frequency breakdown). A common approach to solve this problem is to rely on the loop and star decomposition of the unknowns. Unfortunatelly, building the loops is challenging in many applications, especially in the presence of junctions. In this work, we investigate the effectiveness of quasi-Helmholtz projector approaches in problems containing junctions for curing the low-frequency breakdown without detecting the global loops. Our study suggests that the performance of the algorithms required to obtain the projectors in the presence of junctions is maintained while keeping constant the number of sheets per junction. Finally, with a sequence of numerical tests, this work shows the practical impact of the technique and its applicability to real case scenarios.

Eddy currents are central to several industrial applications and there is a strong need for their efficient modeling. Existing eddy current solution strategies are based on a quasi-static approximation of Maxwell's equations for lossy conducting objects and thus their applicability is restricted to low frequencies. On the other hand, available full-wave solvers such as the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) equation become highly ill-conditioned and inaccurate in eddy current settings. This work presents a new well-conditioned and stable full-wave formulation which encompasses the simulation of eddy currents. Our method is built upon the PMCHWT equation and thus remains valid over the entire frequency range. Moreover, our scheme is also compatible with structures containing holes and handles (multiply connected geometries). The effectiveness of quasi-Helmholtz projectors is leveraged to obtain a versatile solver, which is computationally efficient and allows for a seamless transition between low and high frequencies. The stability and accuracy of the new method are demonstrated both theoretically and through numerical experiments on canonical and realistic structures.

In order to accurately compute scattered and radiated fields in the presence of arbitrary excitations, a low-frequency stable discretization of the right-hand side (RHS) of a quasi-Helmholtz preconditioned electric field integral equation (EFIE) on multiply-connected geometries is introduced, which avoids an ad-hoc extraction of the static contribution of the RHS when tested with solenoidal functions. To obtain an excitation agnostic approach, our ansatz generalizes a technique to multiply-connected geometries where the testing of the RHS with loop functions is replaced by a testing of the normal component of the magnetic field with a scalar potential. To this end, we leverage orientable global loop functions that are formed by a chain of Rao-Wilton-Glisson (RWG) functions around the holes and handles of the geometry, for which we introduce cap surfaces that allow to uniquely define a scalar potential. We show that this approach works with open and closed, orientable and non-orientable geometries. The numerical results demonstrate the effectiveness of this approach.

Biomedical applications of electromagnetics is a fundamental field of interest for the antennas and propagation (AP) community, which is why we have decided to debut a new column called “Bioelectromagnetics,” starting with this issue of IEEE Antennas and Propagation Magazine . I am very grateful to Prof. Asimina Kiourti from the ElectroScience Laboratory of The Ohio State University for agreeing to be the column’s founding editor. The column will focus on biomedical applications of electromagnetics, propagation, and antennas. All of the contributions should be written in the magazine’s style, addressing readers in our entire AP community. If the article’s content and style would make it appropriate for one of our technical publications, including IEEE Journal of Electromagnetics, RF and Microwaves in Medicine and Biology , it is probably not suitable for the magazine. Instead, the contributions should be written to be understandable by a large technical audience so that even those AP members with research interests outside bioelectromagnetism could understand and be cross fertilized by the column’s content. Review articles from recognized experts in their respective fields will be equally welcome. All prospective authors should first contact the column editor or editor-in-chief before preparing their manuscripts to check the compatibility of their perspective contribution with the column’s scope. We await your contributions!