Abstract
A new effective numerical-analytical method of analysis of cylindrical structures with arbitrary cross-section is presented. The method is based on an inversion of the main singular part of an operator equation. The Galerkin method is used with basis functions that are the eigenfunctions of the boundary value problem for the electromagnetic wave diffraction by a circular cylinder. The method was used to investigate diffraction by inhomogeneous dielectric bodies, to treat discontinuities in a waveguide, and to analyze waveguides and strip lines with a complex cross-sections.