Simulation of electromagnetic wave scattering on hollow structures with elliptical cross section

Objective . The aim of the study is to solve a problem aimed at assessing the characteristics of electromagnetic wave scattering on hollow structures whose dimensions belong to the resonant region. Method . The dimensions of the hollow structures with maximum scattering characteristics were determined by a combination of the integral equation method and the optimization method. Scattering at the edges of the aperture of the hollow structure is taken into account. It is proposed to use the Mathieu equation to determine the flow characteristics. The stages of the algorithm for calculating the Mathieu functions are given, which were used during the implementation of the computer program. Parseval's equality is used for the integral transformation. Result . A mathematical model and an algorithm for numerical analysis of the scattering features of plane radio waves on hollow structures that are components of complex-shaped objects, antenna-feeder lines, and antenna devices have been created. The results of test calculations have been obtained. The structure of the subsystem for analyzing complex-shaped hollow structures has been proposed. Conclusion . A priori estimates are obtained for the solution of a boundary value problem in a strip of higher-order elliptic equations degenerating to a cubic equation in one variable. Conditions for achieving a priori estimates are shown; additional spaces are introduced for this purpose. The problem is studied in weighted spaces of the S.L. Sobolev type. Two theorems related to the boundary value problem in a strip for one class of degenerate elliptic equations of high order are considered, and an analysis of the possibilities of obtaining an a priori estimate is carried out. Weighted spaces give an a priori estimate for the solution of a boundary value problem in a strip for a higher-order elliptic equation degenerating to a cubic equation on one of the boundaries of the strip in one of the variables.