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.%%%%Ph.D., Mathematics – Drexel University, 2013
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