Differences between certain solvable and nonsolvable ill-posed integral equations, with the same nonsingular kernel, are discussed. The main results come from constructing a solvable equation in the context of straight thin-wire antennas. The kernel of this equation is the usual approximate (also called reduced) kernel, while its exact solution is the familiar sinusoidal current. Numerical solutions to this solvable equation are compared to corresponding numerical solutions of the usual-Halle¿n and Pocklington-equations with the approximate kernel; it is known from previous publications that these last two equations are nonsolvable and that their numerical solutions present severe oscillations when the number of basis functions is sufficiently large. It is found that the difficulties encountered in the former (solvable) equation are much less important compared to those of the nonsolvable ones. The same conclusion is brought out from other integral equations, arising in different contexts (thin-wire circular-loop antenna, Method of Auxiliary Sources, and straight wire antenna of infinite length). We discuss the consistency of our results with Picard's theorem. The results in this paper supplement previous publications regarding the difficulties of numerically solving thin-wire integral equations with the approximate kernel.

Approximate, non-singular kernels are often used in moment-method formulations coping with thin-wire structures. Their use has important consequences, one of which is the appearance of oscillations in the computed currents when the number of sub-domain basis functions is sufficiently large. These oscillations are not due to round-off errors. In this paper, a smoothing procedure is used in conjunction with Galerkin's formulation with piecewise sinusoidal functions, which yields non-oscillating current distributions. Special attention is paid to the solutions over a wide range of discretization levels (number of basis/testing functions), in order to examine and illustrate the similarities and differences between results obtained with and without the proposed remedy. Finally, a comparison with results derived with the exact kernel is provided.

Fundamental properties of certain popular integral equations for thin-wire circular-loop antennas with nonsingular kernels are studied. The cornerstone of our study is a large-asymptotic formula for the n'th Fourier coefficient of the nonsingular kernel. Four different methods of driving the circular loop are considered; namely, the delta-function generator, the finite-gap generator, a certain type of frill generator, and the case of plane-wave incidence. The excitation model is crucial to our discussions, since it determines the behavior of the solution convergence. Also discussed are associated difficulties that may arise when moment methods are applied to the aforementioned equations, as well as a simple improvement to the Fourier-series method for determining the current in the case of the frill generator. The main results herein closely parallel recent results for the case of the straight antenna, and similarities and differences between the straight and circular cases are discussed.

This paper presents a comprehensive review of research conducted on the Method of Auxiliary Sources (MAS) over a period of the last 22 years, i.e., since the last up-to-date survey was published. MAS is a very attractive numerical technique due to its simple algorithmic structure and the generally low computational cost it requires in terms of memory and CPU time; this is why it has been applied to a vast variety of cases, as concluded by the long citations list included. After a short introduction summarizing the fundamental concepts of the method, references since 2002 are categorized, briefly described, and commented on. This work is intended to assist every researcher who is involved in MAS computations, providing an exhaustive, to the best of the authors’ knowledge, list of related publications.

This paper presents a probabilistic approach for the susceptibility assessment of a straight printed-circuit-board trace in the presence of a random electromagnetic field, which is essentially modeled as a plane wave with parameters (magnitude, polarization angle, direction-of-arrival angles) treated as random variables. Closed-form expressions are derived for the probability density function of the induced far-end voltage in certain cases of field descriptions (excitation scenarios). An easy-to-apply Monte–Carlo approach is employed for comparison and verification purposes, but also to cope with scenarios that are not analytically tractable.

The Method of Auxiliary Sources (MAS) is an established technique for the numerical solution of electromagnetic (EM) scattering and radiation problems. This paper presents a hybrid of MAS with the Fast Multipole Method (FMM), which provides a strategy for reducing the computational cost and for solving large-scale problems without notable accuracy loss (and in a reasonable time). The hybrid MAS-FMM scheme is applied to the problem of EM scattering from an arbitrarily large array of lossless/lossy dielectric cylinders. Numerical results are presented to verify the MAS and MAS-FMM schemes, as well as to illuminate the improvements stemming from the proposed hybridization (especially the ones regarding the associated complexity and computational cost). A few concluding remarks offer a summary of this work, along with a list of possible future extensions.