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

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dc.contributor.advisor Bokil, Vrushali
dc.creator Henderson, Scott Edward
dc.date.accessioned 2008-07-21T20:43:27Z
dc.date.available 2008-07-21T20:43:27Z
dc.date.copyright 2008-06-10
dc.date.issued 2008-07-21T20:43:27Z
dc.identifier.uri http://hdl.handle.net/1957/9027
dc.description Graduation date: 2009 en_US
dc.description.abstract 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. en_US
dc.language.iso en_US en_US
dc.subject Electromagnetic en_US
dc.subject Numerical en_US
dc.subject Analysis en_US
dc.subject Fourth-Order en_US
dc.subject.lcsh Numerical analysis en_US
dc.subject.lcsh Electromagnetic waves -- Mathematical models en_US
dc.title Analysis of fourth order numerical methods for the simulation of electromagnetic waves in dispersive media en_US
dc.type Thesis en_US
dc.degree.name Master of Science (M.S.) in Mathematics en_US
dc.degree.level Master's en_US
dc.degree.discipline Science en_US
dc.degree.grantor Oregon State University en_US
dc.contributor.committeemember Peszynska, Malgorzata
dc.contributor.committeemember Gibson, Nathan
dc.contributor.committeemember Haggerty, Roy

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