Analysis of fourth order numerical methods for the simulation of electromagnetic waves in dispersive media Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/b8515r947

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  • In this thesis, we investigate the problem of simulating Maxwell's equations in dispersive dielectric media. We begin by explaining the relevance of Maxwell's equations to 21st century problems. We also discuss the previous work on the numerical simulations of Maxwell's equations. Introductions to Maxwell's equations and the Yee finite difference scheme follow. Debye and Lorentz dispersive media are then introduced followed by a description of the use of fourth-order accurate spatial derivative approximations. First we consider using fourth-order spatial methods in free-space and the application of the method to the Debye media problem. The fourth-order Debye method is compared to the Yee Debye method using both stability and phase error analyses. After discussions of Debye media approximations, we consider the application of fourth-order methods to Lorentz media. Four schemes are introduced and are called the JHT, KF, HOJHT and HOKF methods. The stability and phase error properties of the HOJHT and HOKF schemes are defined and are compared to the JHT and KF methods. The KF, HOJHT and HOKF schemes are then compared in simulation and are judged based on max-error and processing time. Out of the four schemes, we find that the HOKF scheme is superior to the other three schemes for the simulation of electromagnetic waves in Lorentz media. We also find that the fourth-order accurate schemes have specific advantages over the second-order accurate schemes.
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