Time-domain electromagnetics of waveguide-type open resonators

Abstract

New algorithmic schemes for modeling the problems of linear theory of waveguide discontinuities are presented. Numerical experiment is still the main tool for investigation of the resonant wave scattering phenomena, which are characteristic for such structures. The mathematical approaches employed for such purposes have to satisfy relevant demands for accuracy, efficiency and versatility, and for the ability to be focused on particular details of various practically interesting regimes. The approaches for analyses of transient processes in the waveguide-type open resonators considered here satisfy all these requirements. They rely on the description of the scattering properties of discontinuities in regular waveguides in terms of transform operators related to the evolutionary basis of non-stationary signals that are qualitatively the same for all guiding structures. They suppose an application of the analytical regularization technique at key stages of the solving procedure. The approaches developed can be applied to the solution of a wide range of electromagnetic and acoustic boundary value and initial value problems. The class of considered model problems comprises resonant type discontinuities in circular and coaxial waveguides excited by an axisymmetric TE electromagnetic wave.