The method of regularization in wave scattering and propagation problems

The paper is concerned with the review of mathematical foundations of the method of regularization (MoR) in electromagnetics, and summarizes the information on the solved problems together with some new developments. It is possible to point out three different ways of extracting out an invertible part of the original equation. The first handles static part, the second high-frequency part, and the third exploits frequency-uniform solutions for canonical geometries. Combinations between the last and one of the first two are also possible. Computationally, the best efficiency is achieved if tilded operators are available explicitly, in terms of some elementary or special functions. However, in principle, the whole procedure of inverting, say, the static part can be performed numerically