Hypersingular integral equation of wave diffraction problem on pre-Cantor grating and its discrete mathematical models

Mathematical model of wave diffraction problem H polarized of a plane electromagnetic wave by a pre-Cantor grating, consisting of a finite number of perfectly conducting strips, has been constructed. In the cross section grating plane perpendicular to the edges of the strips, there is a system of intervals obtained on the N-th step on the principle of constructing a Cantor set on the interval [-l,l]. Extensive numerical experiments based on a discrete mathematical model have been carried out. The approximate values of both solutions of integral equations and the vectors of the electromagnetic field have been obtained. The patterns of the field in the far and near zone have been calculated.