Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Electrical Engineering and Computer Science


Atef Z. Elsherbeni

Second Advisor

Jay K. Lee


FDTD, Single-Field, Vector wave equation

Subject Categories



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.


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