On the use of diffusion synthetic acceleration in parallel 3D neutral particle transport calculations

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The linear Boltzmann transport equation (BTE) is an integro-differential equation arising in deterministic models of neutral and charged particle transport. In slab (one-dimensional Cartesian) geometry and certain higher-dimensional cases, Diffusion Synthetic Acceleration (DSA) is known to be an effective algorithm for the iterative solution of the discretized BTE. Fourier and asymptotic analyses have been applied to various idealizations (e.g., problems on infinite domains with constant coefficients) to obtain sharp bounds on the convergence rate of DSA in such cases. While DSA has been shown to be a highly effective acceleration (or preconditioning) technique in one-dimensional problems, it has been observed ... continued below

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992 Kilobytes pages

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Brown, P. & Chang, B. May 14, 1998.

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The linear Boltzmann transport equation (BTE) is an integro-differential equation arising in deterministic models of neutral and charged particle transport. In slab (one-dimensional Cartesian) geometry and certain higher-dimensional cases, Diffusion Synthetic Acceleration (DSA) is known to be an effective algorithm for the iterative solution of the discretized BTE. Fourier and asymptotic analyses have been applied to various idealizations (e.g., problems on infinite domains with constant coefficients) to obtain sharp bounds on the convergence rate of DSA in such cases. While DSA has been shown to be a highly effective acceleration (or preconditioning) technique in one-dimensional problems, it has been observed to be less effective in higher dimensions. This is due in part to the expense of solving the related diffusion linear system. We investigate here the effectiveness of a parallel semicoarsening multigrid (SMG) solution approach to DSA preconditioning in several three dimensional problems. In particular, we consider the algorithmic and implementation scalability of a parallel SMG-DSA preconditioner on several types of test problems.

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992 Kilobytes pages

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  • Super Computing 98, Orlando, FL (US), 11/07/1998--11/13/1998

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  • Report No.: UCRL-JC-130877
  • Report No.: YN0100000
  • Grant Number: W-7405-ENG-48
  • Office of Scientific & Technical Information Report Number: 2775
  • Archival Resource Key: ark:/67531/metadc664051

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  • May 14, 1998

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  • June 29, 2015, 9:42 p.m.

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  • May 6, 2016, 1:48 p.m.

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Brown, P. & Chang, B. On the use of diffusion synthetic acceleration in parallel 3D neutral particle transport calculations, article, May 14, 1998; California. (digital.library.unt.edu/ark:/67531/metadc664051/: accessed September 22, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.