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Dissertation
Asymptotic Analysis of Resonances of Periodic Scatterers
Doctor of Philosophy (Ph.D.), Drexel University
Jun 2022
DOI:
https://doi.org/10.17918/00001124
Abstract
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