Improved criticality convergence via a modified Monte Carlo iteration method

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Nuclear criticality calculations with Monte Carlo codes are normally done using a power iteration method to obtain the dominant eigenfunction and eigenvalue. In the last few years it has been shown that the power iteration method can be modified to obtain the first two eigenfunctions. This modified power iteration method directly subtracts out the second eigenfunction and thus only powers out the third and higher eigenfunctions. The result is a convergence rate to the dominant eigenfunction being |k{sub 3}|/k{sub 1} instead of |k{sub 2}|/k{sub 1}. One difficulty is that the second eigenfunction contains particles of both positive and negative weights ... continued below

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Booth, Thomas E & Gubernatis, James E January 1, 2009.

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Nuclear criticality calculations with Monte Carlo codes are normally done using a power iteration method to obtain the dominant eigenfunction and eigenvalue. In the last few years it has been shown that the power iteration method can be modified to obtain the first two eigenfunctions. This modified power iteration method directly subtracts out the second eigenfunction and thus only powers out the third and higher eigenfunctions. The result is a convergence rate to the dominant eigenfunction being |k{sub 3}|/k{sub 1} instead of |k{sub 2}|/k{sub 1}. One difficulty is that the second eigenfunction contains particles of both positive and negative weights that must sum somehow to maintain the second eigenfunction. Summing negative and positive weights can be done using point detector mechanics, but this sometimes can be quite slow. We show that an approximate cancellation scheme is sufficient to accelerate the convergence to the dominant eigenfunction. A second difficulty is that for some problems the Monte Carlo implementation of the modified power method has some stability problems. We also show that a simple method deals with this in an effective, but ad hoc manner.

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  • Int'l Conf. on Math. Comp. Methods and Reactor Physics ; May 3, 2009 ; Saratoga Springs, NY

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  • Report No.: LA-UR-09-01082
  • Report No.: LA-UR-09-1082
  • Grant Number: AC52-06NA25396
  • Office of Scientific & Technical Information Report Number: 956450
  • Archival Resource Key: ark:/67531/metadc932206

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Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

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  • January 1, 2009

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  • Nov. 13, 2016, 7:26 p.m.

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  • Dec. 9, 2016, 11:41 p.m.

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Booth, Thomas E & Gubernatis, James E. Improved criticality convergence via a modified Monte Carlo iteration method, article, January 1, 2009; [New Mexico]. (digital.library.unt.edu/ark:/67531/metadc932206/: accessed November 20, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.