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Title: Applying nonlinear diffusion acceleration to the neutron transport k-Eigenvalue problem with anisotropic scattering

Abstract

High-order/low-order (or moment-based acceleration) algorithms have been used to significantly accelerate the solution to the neutron transport k-eigenvalue problem over the past several years. Recently, the nonlinear diffusion acceleration algorithm has been extended to solve fixed-source problems with anisotropic scattering sources. In this paper, we demonstrate that we can extend this algorithm to k-eigenvalue problems in which the scattering source is anisotropic and a significant acceleration can be achieved. Lastly, we demonstrate that the low-order, diffusion-like eigenvalue problem can be solved efficiently using a technique known as nonlinear elimination.

Authors:
 [1];  [1];  [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1246339
Report Number(s):
LA-UR-14-28681
Journal ID: ISSN 0029-5639
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
Nuclear Science and Engineering
Additional Journal Information:
Journal Volume: 181; Journal Issue: 3; Journal ID: ISSN 0029-5639
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Mathematics

Citation Formats

Willert, Jeffrey, Park, H., and Taitano, William. Applying nonlinear diffusion acceleration to the neutron transport k-Eigenvalue problem with anisotropic scattering. United States: N. p., 2015. Web. doi:10.13182/NSE14-131.
Willert, Jeffrey, Park, H., & Taitano, William. Applying nonlinear diffusion acceleration to the neutron transport k-Eigenvalue problem with anisotropic scattering. United States. doi:10.13182/NSE14-131.
Willert, Jeffrey, Park, H., and Taitano, William. Sun . "Applying nonlinear diffusion acceleration to the neutron transport k-Eigenvalue problem with anisotropic scattering". United States. doi:10.13182/NSE14-131. https://www.osti.gov/servlets/purl/1246339.
@article{osti_1246339,
title = {Applying nonlinear diffusion acceleration to the neutron transport k-Eigenvalue problem with anisotropic scattering},
author = {Willert, Jeffrey and Park, H. and Taitano, William},
abstractNote = {High-order/low-order (or moment-based acceleration) algorithms have been used to significantly accelerate the solution to the neutron transport k-eigenvalue problem over the past several years. Recently, the nonlinear diffusion acceleration algorithm has been extended to solve fixed-source problems with anisotropic scattering sources. In this paper, we demonstrate that we can extend this algorithm to k-eigenvalue problems in which the scattering source is anisotropic and a significant acceleration can be achieved. Lastly, we demonstrate that the low-order, diffusion-like eigenvalue problem can be solved efficiently using a technique known as nonlinear elimination.},
doi = {10.13182/NSE14-131},
journal = {Nuclear Science and Engineering},
number = 3,
volume = 181,
place = {United States},
year = {2015},
month = {11}
}

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