Award Date

5-1-2017

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematical Sciences

First Committee Member

Jichun Li

Second Committee Member

Monika Neda

Third Committee Member

Hongtao Yang

Fourth Committee Member

Pengtao Sun

Fifth Committee Member

Yi-tung Chen

Number of Pages

128

Abstract

This dissertation investigates three different mathematical models based on the time domain Maxwell's equations using three different numerical methods: a Yee scheme using a non-uniform grid, a nodal discontinuous Galerkin (nDG) method, and a newly developed discontinuous Galerkin method named the weak Galerkin (WG) method. The non-uniform Yee scheme is first applied to an electromagnetic metamaterial model. Stability and superconvergence error results are proved for the method, which are then confirmed through numerical results. Additionally, a numerical simulation of backwards wave propagation through a negative-index metamaterial is given using the presented method. Next, the nDG method is used to simulate signal propagation through a corrugated coaxial cable through the use of axisymmetric Maxwell's equations. Stability and error analysis are performed for the semi-discrete method, and are verified through numerical results. The nDG method is then used to simulate signal propagation through coaxial cables with a number of different corrugations. Finally, the WG method is developed for the standard time-domain Maxwell's equations. Similar to the other methods, stability and error analysis are performed on the method and are verified through a number of numerical experiments.

Keywords

coaxial cable; FEM; Galerkin; Maxwell's Equations; Metamaterial

Disciplines

Electromagnetics and Photonics | Engineering Physics | Mathematics

Language

English

Available for download on Tuesday, May 15, 2018


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