Date of Award

Spring 1-1-2018

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

First Advisor

Melinda Piket-May

Second Advisor

Mohammed Hadi

Third Advisor

Atef Elsherbeni

Fourth Advisor

Edward Kuester

Abstract

This dissertation deals with advanced formulations and applications of finite difference time domain (FDTD) method. This is composed of four themes. The first deals with the development of a plane wave excitation formulation in FV24, a finite-volume based higher-order FDTD variant. With its excellent phase error performance even for coarse grid, FV24 can be applied to electrically large problems. The plane wave excitation method based on Total field/Scattered field formulation and Discrete planewave technique is demonstrated and validated for FV24. In the latter part of this work different near to farfield transformation approaches possible in FDTD are compared for accuracy.

The second part of the research deals with application of FDTD to glass weave-induced skew (GWS) problem. The GWS on a differential pair can cause increased bit error rates affecting the robustness of the digital system, and increased radiated emissions causing compliance failures. The frequency dependence of glass and resin materials properties are modeled using auxiliary differential equation formulation for FDTD, to estimate GWS on a differential pair. The skew numbers are benchmarked with the available commercial solvers. Also, the use of graphical processing units (GPUs) to accelerate the skew simulations is demonstrated.

The third part of the research deals with the derivation of numerical dispersion relation (NDR) for spherical FDTD, and the sensitivity study of the associated numerical wave number. Elementary functions native to spherical coordinates are used in the derivation of the numerical dispersion. Given the non-uniform nature of the spherical FDTD grid, the NDR and the corresponding numerical wave number are shown to be position dependent. The latter part of this research includes a study to derive the stability criterion for spherical FDTD and challenges involved therein.

The final part of the research studies the effectiveness of different absorbing boundary condition formulations for spherical FDTD in absorbing the waves. It is shown that the split-field formulation of perfectly matched layer (PML) is not as effective as stretched-coordinate formulation. This work includes derivation of continuous-space PML reflection coefficient, update equations for implementation of stretched-coordinate PML in spherical FDTD and analysis of reflection error for different PML parameters.

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