Dissertation/Thesis Abstract

Hybrid Deterministic/Monte Carlo Methods for Solving the Neutron Transport Equation and k-Eigenvalue Problem
by Willert, Jeffrey Alan, Ph.D., North Carolina State University, 2013, 223; 3575891
Abstract (Summary)

The goal of this thesis is to build hybrid deterministic/Monte Carlo algorithms for solving the neutron transport equation and associated k-eigenvalue problem. We begin by introducing and deriving the transport equation before discussing a series of deterministic methods for solving the transport equation. To begin we consider moment-based acceleration techniques for both the one and two-dimensional fixed source problems. Once this machinery has been developed, we will apply similar techniques for computing the dominant eigenvalue of the neutron transport equation. We'll motivate the development of hybrid methods by describing the deficiencies of deterministic methods before describing Monte Carlo methods and their advantages. We conclude the thesis with a chapter describing the detailed implementation of hybrid methods for both the fixed-source and k-eigenvalue problem in both one and two space dimensions. We'll use a series of test problems to demonstrate the effectiveness of these algorithms before hinting at some possible areas of future work.

Indexing (document details)
Advisor: Kelley, C. T.
Commitee: Azmy, Yousry, Hoefer, Mark, Knoll, Dana
School: North Carolina State University
Department: Applied Mathematics
School Location: United States -- North Carolina
Source: DAI-B 75/03(E), Dissertation Abstracts International
Subjects: Applied Mathematics
Keywords: Eigenvalue, Neutron transport, Newtons method, Numerical analysis
Publication Number: 3575891
ISBN: 978-1-303-54905-2
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