Oblique Scattering/hybrid Wave Propagation In Elliptical Homogeneous Configurations & Spectrum/preconditioning Of The Singular Domain Integral Equation

Abstract

This doctoral dissertation is oriented on two directions: exact techniques based on analytical expressions, and numerical techniques. Initially, the problem of the electromagnetic scattering by dielectric elliptical cylinders, under oblique illumination, is studied. The problem is solved using the elliptical wavefunctions. The cross sections of the problem are calculated. Then the corresponding inner problem. i.e. of hybrid wave propagation in dielectric elliptical waveguides. The cutoff wavenumbers are calculated exact and analytically. Finally, the singular domain integral equation is solved numerically, the spectrum of the singular operator is obtained, and preconditioning techniques are applied for the GMRES algorithm.