Doctor of Philosophy (PhD)
First Committee Member
Second Committee Member
Third Committee Member
Fourth Committee Member
Fifth Committee Member
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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.
coaxial cable; FEM; Galerkin; Maxwell's Equations; Metamaterial
Electromagnetics and Photonics | Engineering Physics | Mathematics
Shields, Sidney, "Novel Methods for the Time-Dependent Maxwell’s Equations and their Applications" (2017). UNLV Theses, Dissertations, Professional Papers, and Capstones. 3031.