An Sn Application of Homotopy Continuation in Neutral Particle Transport

The objective of this dissertation is to investigate the usefulness of homotopy continuation applied in the context of neutral particle transport where traditional methods of acceleration degrade. This occurs in higher dimensional heterogeneous problems [51]. We focus on utilizing homotopy continuation as a means of providing a better initial guess for difficult problems. We investigate various homotopy formulations for two primary diffcult problems: a thick-diffusive fixed internal source, and a k-eigenvalue problem with high dominance ratio. We also investigate the usefulness of homotopy continuation for computationally intensive problems with 30-energy groups. We find that homotopy continuation exhibits usefulness in specific problem formulations. In the thick-diffusive problem it shows benefit when there is a strong internal source in thin materials. In the k-eigenvalue problem, homotopy continuation provides an improvement in convergence speed for fixed point iteration methods in high dominance ratio problems. We also show that one of our imbeddings successfully stabilizes the nonlinear formulation of the k-eigenvalue problem with a high dominance ratio.

Name thesis:degree_name

Nuclear Engineering

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Nuclear Engineering

Year

2014

Author dc:creator

• Myers, Nicholas

Contributors dc:contributor

• Prinja, Anil
• Warsa, Jim
• Coutsias, Evangelos
• De Oliveira, Cassiano

• Homotopy
• Sn
• Continuation
• Transport
• Eigenvalue
• Diffusive

Language dc:language

English

Identifier

https://digitalrepository.unm.edu/ne_etds/10

OAI identifier oai:identifier

oai:digitalrepository.unm.edu:ne_etds-1009