We consider the asymptotic analysis of the resonances of a bounded scatterer with a periodic index of refraction with small period size [epsilon] for the scalar Helmholtz equation. The resonance problem is formulated as a nonlinear eigenvalue problem, for which we can derive formulas when the homogenized resonance is simple provided a conjecture about the operators hold. In this case we have an explicit formula for the first order corrections and find that they are nontrivial in general. For convex polygonal scatterers of rational normal, the resonances converge only O([epsilon]), even for scatterers which are unions of period cells. For smooth domains with no flat parts the resonances converge o([epsilon]), but the convergence is nonetheless sub-quadratic in general. Numerical experiments in one and two dimensions are presented along with the convergence rates which support our conjecture.
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Details
Title
Asymptotic Analysis of Resonances of Periodic Scatterers
Creators
Alexander Joseph Furia
Contributors
Shari Moskow (Advisor)
Awarding Institution
Drexel University
Degree Awarded
Doctor of Philosophy (Ph.D.)
Publisher
Drexel University; Philadelphia, Pennsylvania
Number of pages
ix, 97 pages
Resource Type
Dissertation
Language
English
Academic Unit
College of Arts and Sciences; Drexel University; Mathematics
Other Identifier
991018527002604721
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