| In this dissertation, a set of general purpose single-field finite-difference time-domain updating equations for solving electromagnetic problems is derived. The formulation uses a single-field expression for full-wave solution. This formulation can provide numerical results similar to those obtained using the traditional formulation with less required computer resources.;Traditional finite-difference time-domain updating equations are based on Maxwell's curl equations whereas the single-field updating equations used here are based on the vector wave equation. General formulations are derived for normal and oblique incidence plane wave cases for linear, isotropic, homogeneous and non-dispersive as well as dispersive media.;To compare the single-field updating equations with the traditional ones, two-dimensional transverse magnetic, two-dimensional transverse electric and one-dimensional electromagnetic problems are solved. Fields generated by a current sheet and a filament electric current are calculated for one and two-dimensional formulations, respectively. Performance analyses of the single-field formulation in terms of CPU time, memory requirement, stability, dispersion, and accuracy are presented. Based on the simulations of several two-dimensional problems excited by a filament of electric current, it was observed that the single-field method is more efficient than the traditional one in terms of speed and memory requirements.;One scattering problem consisting of three infinitely long dielectric cylinders excited by an obliquely incident plane wave and another scattering problem consisting of a point source exciting a dispersive sphere, utilizing Lorentz-Drude model, are also formulated and analyzed. The numerical results obtained confirmed the validity and efficiency of the single-field formulations. |
