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Electromagnetics and Photonics
University of Nevada, Las Vegas
UNLV Theses, Dissertations, Professional Papers, and Capstones
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Novel Methods For The Time-Dependent Maxwell’S Equations And Their Applications, Sidney Shields
Novel Methods For The Time-Dependent Maxwell’S Equations And Their Applications, Sidney Shields
UNLV Theses, Dissertations, Professional Papers, and Capstones
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 …