Novel methods for the time-dependent Maxwell's equations and their applications
- Univ. of Nevada, Las Vegas, NV (United States)
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.
- Research Organization:
- National Security Technologies, LLC. (NSTec), Mercury, NV (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP) (NA-10)
- DOE Contract Number:
- AC52-06NA25946
- OSTI ID:
- 1352142
- Report Number(s):
- DOE/NV/25946--3178
- Country of Publication:
- United States
- Language:
- English
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