Graduate Thesis Or Dissertation
 

Operator splitting methods for Maxwell's equations in dispersive media

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/mp48sg27s

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  • Accurate modeling and simulation of wave propagation in dispersive dielectrics such as water, human tissue and sand, among others, has a variety of applications. For example in medical imaging, electromagnetic waves are used to interrogate human tissue in a non-invasive manner to detect anomalies that could be cancerous. In non-destructive evaluation of materials, such interrogation is used to detect defects in these materials. In this thesis we present the construction and analysis of two novel operator splitting methods for Maxwell's equations in dispersive media of Debye type which are used to model wave propagation in polar materials like water and human tissue. We construct a sequential and a symmetrized operator splitting scheme which are first order, and second order, respectively, accurate in time. Both schemes are second order accurate in space. The operator splitting methods are shown to be unconditionally stable via energy techniques. Their accuracy and stability properties are compared to established schemes like the Yee or FDTD scheme and the Crank-Nicolson scheme. Finally, results of numerical simulations are presented that confirm the theoretical analysis.
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