Computational modeling of hypersingular integral equations for 2D pre-cantor scattering structure

This paper presents the investigative study to derive a computational model based on hypersingular integral equations for the pre-Cantor plane-parallel diffraction structure. Such structure consists of finite numbers of the thin impedance strips located in the XY plane. A plane transverse magnetic wave is incident from infinity on considered diffraction structure at an angle and need to find the total field resulting from the scattering. The model which is considered in this work is an approximation of real fractal antennas in two-dimensional case. Pre-fractal properties of grating allow producing the newest antennas for modern mobile devices due to their compact size and broadband properties. The purpose of this work is to develop computer model their structure using parametric representation of hypersingular integral operator, Nystrom method with specific quadrature formulas. The numerical results have been obtained and investigated for pre-Cantor structures for calculating physics characteristics. These results have been compared and analyzed in different mathematical models and softwares.