Dissertation/Thesis Abstract

A class of staggered grid algorithms and analysis for time-domain Maxwell systems
by Charlesworth, Alexander E., M.S., Colorado School of Mines, 2016, 91; 10010857
Abstract (Summary)

We describe, implement, and analyze a class of staggered grid algorithms for efficient simulation and analysis of time-domain Maxwell systems in the case of heterogeneous, conductive, and nondispersive, isotropic, linear media. We provide the derivation of a continuous mathematical model from the Maxwell equations in vacuum; however, the complexity of this system necessitates the use of computational methods for approximately solving for the physical unknowns. The finite difference approximation has been used for partial differential equations and the Maxwell Equations in particular for many years. We develop staggered grid based finite difference discrete operators as a class of approximations to continuous operators based on second order in time and various order approximations to the electric and magnetic field at staggered grid locations. A generalized parameterized operator which can be specified to any of this class of discrete operators is then applied to the Maxwell system and hence we develop discrete approximations through various choices of parameters in the approximation. We describe analysis of the resulting discrete system as an approximation to the continuous system. Using the comparison of dispersion analysis for the discrete and continuous systems, we derive a third difference approximation, in addition to the known (2, 2) and (2, 4) schemes. We conclude by providing the comparison of these three methods by simulating the Maxwell system for several choices of parameters in the system

Indexing (document details)
Advisor: Ganesh, Mahadevan
Commitee: Pankavich, Stephen, Tenorio, Luis
School: Colorado School of Mines
Department: Applied Mathematics and Statistics
School Location: United States -- Colorado
Source: MAI 55/03M(E), Masters Abstracts International
Subjects: Applied Mathematics, Electromagnetics
Keywords: Computational electrodynamics, Finite difference time domain
Publication Number: 10010857
ISBN: 978-1-339-46868-6
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