Bulygin V. Mathematical models of electromagnetic waves scattering in space and numerical experiment

Object of the research is the scattering of electromagnetic waves on a perfectly electrically conducting surface of rotation and on a perfectly conducting plane screen located on a boundary between two media. Aim of the research is development of mathematical models of indicated objects. The thesis contains applications of mathematical physics, mathematical analysis, differential equation, linear algebra, computational methods, and in particular the method of discrete singularities. For the first time the problem of an electromagnetic wave diffraction by the rotation surface with arbitrary smooth contour is reduced to the set of one-dimensional hypersingular and singular integral equations with variable coefficients. The method of discrete singularities were used for such set numerical decision for the first time. The approximate solution convergence to exact solutions theorems were proved in the respective Hilbert spaces. For the first time the problem of electromagnetic wave diffraction on a perfectly conducting plane screen located on a boundary between two media is reduced to a system of two-dimensional hypersingular integral equations relative to the functions using which all physical characteristics are expressed. Based on the developed mathematical models of diffraction and the method of discrete singularities a software has been developed, that can perform numerical analysis of various multireflector antennas three-dimensional mathematical models. The developed technique is planned to be applied in various fields of the reflector antenna technology for effective optimization of real-life multireflector antenna systems.