Yatsyk M. Models and computational methods for the investigation of nonlinear layered electrodynamic structures

Solving problems of scattering and generation waves by means of nonlinear layered electrodynamic structures in the resonant frequency range. To the dissertation purpose is construction of computational methods and process research of scattering and generation waves by means of nonlinear layered electrodynamic structures in the resonant frequency range. In the dissertation, a solution to a challenging scientific and practical problem of developing a mathematical model and computational methods for solving boundary value problems of scattering and generation of third harmonic waves by means of nonlinear layered electrodynamic structures in the resonant frequency range is proposed. The problem is based on solving an equivalent system of complex nonlinear integral Hammerstein equations, which, using quadrature formulas, is reduced to a system of complex nonlinear algebraic equations of the second kind. The developed algorithm for the numerical analysis is based on a self-consistent approach, that is, an iterative method based on block-iterative procedures. In the work, algorithms are also constructed and the induced spectral problems are investigated at the frequencies of radiation (scattering and generation) - that is spectral problems with layers of induced dielectric permeability. The combination of self-consistent and spectral analysis made it possible, for the first time, within the framework of a unified approach, to study nonlinear resonance processes at the frequencies of resonant scattering and generation of oscillations, choosing as the excitation frequencies the quantities determined by the real parts of the complex eigen frequencies of the induced spectral problems. Criteria for evaluating the reliability of calculations are given: conditions for fulfilling the energy balance law; estimates of the condition number of the matrices of the radiation problems via the sensitivity of the self-consistent analysis to computational errors, as well as investigation of the matrices of induced spectral problems for degeneracy. Developed in the dissertation mathematics models and obtained results implemented in the scientific research of state budget on themes: "Generation, amplification, detection and propagation of terahertz radiation: electrodynamic modeling and experiment", "New theoretical and experimental methods in electrodynamic modeling, generation and radiation of electromagnetic waves of the GHz and THz (terahertz) range" which used within themes plans scientific research works in department of diffraction theory and diffraction electronics O.Ya. Usikov Institute for Radiophysics and Electronics National Academy of Sciences of Ukraine (IRE NASU) also in educational process in preparation of postgraduate students which study in the discipline "Selected issues of modern theoretical radiophysics" in IRE O.Ya. Usikov NASU. The results obtained in this work are related to the implementation of international programs jointly conducted by the National Academy of Sciences of Ukraine and the Swedish Institute. Grant the Visby Program of the Swedish Institute, Project title: "Advanced solution techniques for large – scale problems aimed at supercomputers and parallels computations".