A spectral analysis of the domain decomposed Monte Carlo method for linear systems
The domain decomposed behavior of the adjoint NeumannUlam Monte Carlo method for solving linear systems is analyzed using the spectral properties of the linear oper ator. Relationships for the average length of the adjoint random walks, a measure of convergence speed and serial performance, are made with respect to the eigenvalues of the linear operator. In addition, relationships for the effective optical thickness of a domain in the decomposition are presented based on the spectral analysis and diffusion theory. Using the effective optical thickness, the Wigner rational approxi mation and the mean chord approximation are applied to estimate the leakage frac tion of random walks from a domain in the decomposition as a measure of parallel performance and potential communication costs. The onespeed, twodimensional neutron diffusion equation is used as a model problem in numerical experiments to test the models for symmetric operators with spectral qualities similar to light water reactor problems. We find, in general, the derived approximations show good agreement with random walk lengths and leakage fractions computed by the numerical experiments.
 Authors:

^{[1]};
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 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Univ. of Wisconsin, Madison, WI (United States)
 Publication Date:
 Grant/Contract Number:
 AC0500OR22725
 Type:
 Accepted Manuscript
 Journal Name:
 Nuclear Engineering and Design
 Additional Journal Information:
 Journal Volume: 295; Journal Issue: C; Journal ID: ISSN 00295493
 Publisher:
 Elsevier
 Research Org:
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Sponsoring Org:
 USDOE Office of Science (SC)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING
 OSTI Identifier:
 1265476
 Alternate Identifier(s):
 OSTI ID: 1247411
Slattery, Stuart R., Evans, Thomas M., and Wilson, Paul P. H.. A spectral analysis of the domain decomposed Monte Carlo method for linear systems. United States: N. p.,
Web. doi:10.1016/j.nucengdes.2015.07.054.
Slattery, Stuart R., Evans, Thomas M., & Wilson, Paul P. H.. A spectral analysis of the domain decomposed Monte Carlo method for linear systems. United States. doi:10.1016/j.nucengdes.2015.07.054.
Slattery, Stuart R., Evans, Thomas M., and Wilson, Paul P. H.. 2015.
"A spectral analysis of the domain decomposed Monte Carlo method for linear systems". United States.
doi:10.1016/j.nucengdes.2015.07.054. https://www.osti.gov/servlets/purl/1265476.
@article{osti_1265476,
title = {A spectral analysis of the domain decomposed Monte Carlo method for linear systems},
author = {Slattery, Stuart R. and Evans, Thomas M. and Wilson, Paul P. H.},
abstractNote = {The domain decomposed behavior of the adjoint NeumannUlam Monte Carlo method for solving linear systems is analyzed using the spectral properties of the linear oper ator. Relationships for the average length of the adjoint random walks, a measure of convergence speed and serial performance, are made with respect to the eigenvalues of the linear operator. In addition, relationships for the effective optical thickness of a domain in the decomposition are presented based on the spectral analysis and diffusion theory. Using the effective optical thickness, the Wigner rational approxi mation and the mean chord approximation are applied to estimate the leakage frac tion of random walks from a domain in the decomposition as a measure of parallel performance and potential communication costs. The onespeed, twodimensional neutron diffusion equation is used as a model problem in numerical experiments to test the models for symmetric operators with spectral qualities similar to light water reactor problems. We find, in general, the derived approximations show good agreement with random walk lengths and leakage fractions computed by the numerical experiments.},
doi = {10.1016/j.nucengdes.2015.07.054},
journal = {Nuclear Engineering and Design},
number = C,
volume = 295,
place = {United States},
year = {2015},
month = {9}
}