Simulation of Localized Surface Plasmon Resonances via DNOs and IIOs

This thesis focuses on simulating scattering returns of electromagnetic radiation from bounded obstacles and the Localized Surface Plasmon Resonances. We present High–Order Perturbation of Surfaces algorithms for the simulation of such configurations, formulated with Dirichlet-Neumann Operators and Impedance–Impedance Operators. With an implementation of these approaches we demonstrate the stable, robust, and highly accurate properties of our algorithms. We also demonstrate the validity and utility of our approaches with a sequence of numerical experiments. Moreover, we show how our formulation delivers a straightforward proof of existence, uniqueness, and analyticity of solutions.