The Cauchy method of analytical regularisation in the modelling of plane wave scattering by a flat pre‐fractal system of impedance strips

Abstract

The Cauchy method of analytical regularisation, first in full explanation, is used for the modelling of the plane wave scattering by a flat pre-fractal system of impedance strips. It is based on a modification of the singular integral equation technique and the correct type of inversion formula of the simplest Cauchy singular integral equation. The approach is effective for the plane H-polarised electromagnetic (or sonic) wave scattering problems. The principle of strict mathematical orderings of the pre-fractal strip grating deals with a five-parts class of perfect fractal sets, which is characterised by a variable positive fractal dimension. Considerable attention is devoted to the asymptotic model of the plane wave scattering by a sparsely filled grating, which has an explicit solution. This result is very important for verification of the mathematical models presented and testing of direct numerical methods. The scattered electromagnetic field in the far zone is successfully analysed with the aid of the asymptotic solution derived for electrically narrow strips.