The method of analytical regularization in wave-scattering and eigenvalue problems: Foundations and review of solutions

On the rugged terrain of today's computational electromagnetics, the univer sal rope-way of MoM and industrial rock-climbing with FDTD electric hammers are necessary technologies. However, a free-style solo climb at the Everes t of analytical regularization is still a fascinating achievement. Here, we discuss the foundations and state-of-the-art of the Method of Analytical R egularization (also called the semi-inversion method). This is a collective name for a family of methods based on conversion of a first-kind or strong ly-singular second-kind integral equation to a second-kind integral equatio n with a smoother kernel, to ensure point-wise convergence of the usual dis cretization schemes. This is done using analytical inversion of a singular part of the original equation; discretization and semi-inversion can be com bined in one operation. Numerous problems being solved today with this appr oach are reviewed, although in some of them, MAR comes in disguise.