Analysis and performance of adjacent-cell preconditioners for accelerating multidimensional transport calculations

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The formal development of the Adjacent-cell Preconditioner (AP) and its implementation in the TORT code are briefly reviewed. Based on earlier experience with diffusion type acceleration, and excellent results in slab geometry the reciprocal averaging formula is used to mix the preconditioner elements across material and mesh discontinuities. Numerical testing of the method employing the Burre Suite of Test Problems (BSTeP), a collection of 144 cases covering a wide range in parameter space, using AP, Partial Current Rebalance (PCR), and TWODANT`s Diffusion Synthetic Acceleration (DSA) is presented. While AP outperforms the other two methods for the majority of the cases ... continued below

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13 p.

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Azmy, Y.Y. December 31, 1996.

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Description

The formal development of the Adjacent-cell Preconditioner (AP) and its implementation in the TORT code are briefly reviewed. Based on earlier experience with diffusion type acceleration, and excellent results in slab geometry the reciprocal averaging formula is used to mix the preconditioner elements across material and mesh discontinuities. Numerical testing of the method employing the Burre Suite of Test Problems (BSTeP), a collection of 144 cases covering a wide range in parameter space, using AP, Partial Current Rebalance (PCR), and TWODANT`s Diffusion Synthetic Acceleration (DSA) is presented. While AP outperforms the other two methods for the majority of the cases included in BSTeP it consumes many more iterations than can be explained by spectral analysis of the homogeneous model problem in cases with sharp material discontinuity. In order to verify this undesirable behavior and explore potential remedies a model problem, the Periodic Horizontal Interface (PHI), is developed that permits discontinuity of nuclear properties and cell height across the interface. Fourier mode decomposition is applied to AP with the reciprocal averaging mixing formula for the PHI configuration and shown to possess a spectral radius that approaches unity as the material discontinuity gets larger. The question of whether an unconditionally stable AP exists for PHI is tackled and preliminary indications are negative. Novel preconditioners that have nontraditional cell-coupling schemes that remain stable in these regimes may have to be sought.

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13 p.

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INIS; OSTI as DE97001731

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  • Seminar on 3D deterministic radiation transport computer programs, features, applications and perspectives, Paris (France), 2-3 Dec 1996

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  • Other: DE97001731
  • Report No.: CONF-961245--2
  • Grant Number: AC05-96OR22464
  • Office of Scientific & Technical Information Report Number: 425361
  • Archival Resource Key: ark:/67531/metadc685420

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

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  • December 31, 1996

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  • July 25, 2015, 2:20 a.m.

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  • Jan. 15, 2016, 12:42 p.m.

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Azmy, Y.Y. Analysis and performance of adjacent-cell preconditioners for accelerating multidimensional transport calculations, article, December 31, 1996; Tennessee. (digital.library.unt.edu/ark:/67531/metadc685420/: accessed December 17, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.