Dissertation
Forward and inverse Born series for diffuse, scalar, and electromagnetic waves
Doctor of Philosophy (Ph.D.), Drexel University
Jun 2013
DOI:
https://doi.org/10.17918/etd-4197
Abstract
In this thesis, we study the forward and inverse scattering problems for three different cases: diffuse, scalar, and electromagnetic waves. We utilize the so called Born series to model solutions to the direct problems and the related inverse Born series as an inversion method. We analyze the convergence of the Born series and the inverse Born series in all cases. We also study some numerical simulations of solutions to these problems. In particular, for the case of electromagnetic waves, we prove several estimates which allow us to find bounds for the Born series operators. We also code a 3-D Maxwell forward solver using a new integral formulation.
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Details
- Title
- Forward and inverse Born series for diffuse, scalar, and electromagnetic waves
- Creators
- Kimberly Nolan - 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
- 4197; 991014632824904721