Abstract

This dissertation presents developed numerical tools for investigating waveguides and resonators' properties for microwave and terahertz technology. The electromagnetics analysis requires solving complex eigenvalue problems, representing various parameters such as resonant frequency or propagation coefficient. Solving equations with eigenvalue boils down to finding the roots of the determinant of the matrix. At the beginning, one presents examples of electromagnetic problems. The following chapter investigates the effectiveness and limitations of currently available global root-finding algorithms and presents improvements to the Global Complex Roots and Poles Finding (GRPF). The proposed self-adaptive initial mesh generator for the GRPF algorithm enables the faster and more accurate zero/pole finding of complex functions. The optimization of the tracing method is proposed based on the self-adaptive discretization of Cauchy's argument principle. The limitations of tracing and the multipath problem are also discussed. Finally, a new approach to determining the curves representing roots as a function of an extra parameter is presented. The techniques proposed in each chapter reduce the analysis time and enhance the accuracy of the results. The developed tools for solving nonlinear eigenvalue problems can also be applied in other engineering fields.

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