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Title: Efficient solution of the simplified P N equations

Abstract

We show new solver strategies for the multigroup SPN equations for nuclear reactor analysis. By forming the complete matrix over space, moments, and energy a robust set of solution strategies may be applied. Moreover, power iteration, shifted power iteration, Rayleigh quotient iteration, Arnoldi's method, and a generalized Davidson method, each using algebraic and physics-based multigrid preconditioners, have been compared on C5G7 MOX test problem as well as an operational PWR model. These results show that the most ecient approach is the generalized Davidson method, that is 30-40 times faster than traditional power iteration and 6-10 times faster than Arnoldi's method.

Authors:
 [1];  [1]
  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1185441
Alternate Identifier(s):
OSTI ID: 1244284
Grant/Contract Number:
AC05-00OR22725; DEAC05-00OR22725
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 284; Journal Issue: C; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; radiation transport; nuclear criticality; eigenvalue solvers

Citation Formats

Hamilton, Steven P., and Evans, Thomas M. Efficient solution of the simplified PN equations. United States: N. p., 2014. Web. doi:10.1016/j.jcp.2014.12.014.
Hamilton, Steven P., & Evans, Thomas M. Efficient solution of the simplified PN equations. United States. doi:10.1016/j.jcp.2014.12.014.
Hamilton, Steven P., and Evans, Thomas M. Tue . "Efficient solution of the simplified PN equations". United States. doi:10.1016/j.jcp.2014.12.014. https://www.osti.gov/servlets/purl/1185441.
@article{osti_1185441,
title = {Efficient solution of the simplified PN equations},
author = {Hamilton, Steven P. and Evans, Thomas M.},
abstractNote = {We show new solver strategies for the multigroup SPN equations for nuclear reactor analysis. By forming the complete matrix over space, moments, and energy a robust set of solution strategies may be applied. Moreover, power iteration, shifted power iteration, Rayleigh quotient iteration, Arnoldi's method, and a generalized Davidson method, each using algebraic and physics-based multigrid preconditioners, have been compared on C5G7 MOX test problem as well as an operational PWR model. These results show that the most ecient approach is the generalized Davidson method, that is 30-40 times faster than traditional power iteration and 6-10 times faster than Arnoldi's method.},
doi = {10.1016/j.jcp.2014.12.014},
journal = {Journal of Computational Physics},
number = C,
volume = 284,
place = {United States},
year = {Tue Dec 23 00:00:00 EST 2014},
month = {Tue Dec 23 00:00:00 EST 2014}
}

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