Nosych A. Mathematical Modeling in the Analysis and Synthesis of Multi-Reflector Quasioptical Antennas and Open Beam Waveguides

Object of the research is the radiation, transmission, scattering and focusing of electromagnetic waves with the help of one or more thin metal reflectors. Aim of the research is development and validation of mathematical models of multireflector antenna systems: the systems of singular integral equations of the first kind, which are obtained by reducing the diffraction problem in the E-polarization case on two-dimensional contours of arbitrary smooth shape and of arbitrary amount. Numerical simulations were carried out to optimize the electrodynamic performance of reflector antennas and waveguides. The thesis contains applications of mathematical physics, theory of integral and differential equations, linear algebra, computational methods, and in particular the method of discrete singularities, and also object-oriented programming. For the first time the developed method of discrete singularities is applied to mathematical modelling of two-dimensional multireflector antennas in the case of E-polarization by reducing a system of coupled singular integral equations of the diffraction problem. The method of discrete singularities is applied to numerical simulation and modelling of quasioptical multireflector antennas with arbitrarily amount of reflectors, open beam waveguides and flat metal plate lens antennas. For the first time the method of discrete singularities is applied to the inverse problem for the numerical synthesis of the reflector antenna profile by the field, which is given its near zone at a certain comparison contour. A series of numerical experiments are carried out to build the reflector shape synthesis: to obtain a quasioptical beam splitter. Based on the developed mathematical models of diffraction and the method of discrete singularities a software has been developed, that can perform numerical analysis, optimisation and synthesis of mathematical models of various multireflector antennas. 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.