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Dissertation
Asymptotic methods in inverse scattering
Doctor of Philosophy (Ph.D.), Drexel University
01 Jun 2015
DOI:
https://doi.org/10.17918/etd-6379
Abstract
This work consists of two major components. First, we characterize the effect of a small inhomogeneity on the transmission eigenvalues of a media by deriving an asymptotic expansion. We consider the case of a scalar isotropic media and approach the problem through a variational framework in order to apply tools from the theory of compact operators. Then, we present approximations to the scattered field of the full time-harmonic Maxwell equations with a thin high contrast dielectric scatterer present. Using this approximation, we develop an inversion method to recover the location of the scatterer in a two dimensional plane. We end by presenting numerical simulations demonstrating both the asymptotic result and the efficiency of the inversion method.
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Details
- Title
- Asymptotic methods in inverse scattering
- Creators
- Scott Rome - DU
- Contributors
- Shari Moskow (Advisor) - Drexel University (1970-)
- Awarding Institution
- Drexel University
- Degree Awarded
- Doctor of Philosophy (Ph.D.)
- Publisher
- Drexel University; Philadelphia, Pennsylvania
- Resource Type
- Dissertation
- Language
- English
- Academic Unit
- College of Arts and Sciences; Drexel University; Mathematics
- Other Identifier
- 6379; 991014632208904721