Date of Award

Spring 2021

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Applied Mathematics

First Advisor

Kluger, Yuval

Abstract

In this dissertation, we develop an efficient algorithm to evaluate the azimuthal Fourier components of the Green’s function for the Helmholtz equation in cylindrical coordinates. A computationally efficient algorithm for this modal Green’s function is essential for solvers for electromagnetic scattering from bodies of revolution (e.g., radar cross sections, antennas). Current algorithms to evaluate this modal Green’s function become computationally intractable when the source and target are close or when the wavenumber is large. Furthermore, most of the state of the art methods cannot easily be parallelized. In this work, we present an algorithm for evaluating the modal Green’s function that has performance independent of both source-to-target proximity and wavenumber, and whose cost grows as O(m). Furthermore, our algorithm is embarrassingly parallelizable.

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