Iterative stability analysis of spatial domain decomposition based on block Jacobi algorithm for the diamond-difference scheme

Anistratov, Dmitriy Y.; Azmy, Yousry Y.

doi:10.1016/j.jcp.2015.05.033

Title: Iterative stability analysis of spatial domain decomposition based on block Jacobi algorithm for the diamond-difference scheme

Abstract

Here, we study convergence of the integral transport matrix method (ITMM) based on a parallel block Jacobi (PBJ) iterative strategy for solving particle transport problems. The ITMM is a spatial domain decomposition method proposed for massively parallel computations. AFourier analysis of the PBJ-based iterations applied to SN diamond-difference equations in 1D slab and 2D Cartesian geometries is performed. It is carried out for infinite-medium problems with homogeneous material properties. To analyze the performance of the ITMM with the PBJ algorithm and evaluate its potential in scalability we consider a limiting case of one spatial cell per subdomain. The analysis shows that in such limit the spectral radius of the iteration method is one without regard to values of the scattering ratio and optical thickness of the spatial cells. This implies lack of convergence in infinite medium. Numerical results of finite-medium problems are presented. They demonstrate effects of finite size of spatial domain on the performance of the iteration algorithm as well as its asymptotic behavior when the extent of the spatial domain increases. Finally, these numerical experiments also show that for finite domains iterative convergence to a finite criterion is achievable in a multiple of the sum of number ofmore » cells in each dimension.« less

Authors:

Anistratov, Dmitriy Y. ^[1]; Azmy, Yousry Y. ^[1]

North Carolina State University, Raleigh, NC (United States)

Publication Date:: Thu May 28 00:00:00 EDT 2015

Research Org.:: North Carolina State Univ., Raleigh, NC (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1437429

Alternate Identifier(s):: OSTI ID: 1249985

Grant/Contract Number:: NA0002576; AC07-05ID14517

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Computational Physics

Additional Journal Information:: Journal Volume: 297; Journal Issue: C; Journal ID: ISSN 0021-9991

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; particle transport equation; radiative transfer equation; domain decomposition; iterative methods; Fourier analysis

Citation Formats


                    Anistratov, Dmitriy Y., and Azmy, Yousry Y. Iterative stability analysis of spatial domain decomposition based on block Jacobi algorithm for the diamond-difference scheme.  United States: N. p., 2015. 
Web.  doi:10.1016/j.jcp.2015.05.033.

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                    Anistratov, Dmitriy Y., & Azmy, Yousry Y. Iterative stability analysis of spatial domain decomposition based on block Jacobi algorithm for the diamond-difference scheme.  United States.  https://doi.org/10.1016/j.jcp.2015.05.033

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                    Anistratov, Dmitriy Y., and Azmy, Yousry Y. Thu .  
"Iterative stability analysis of spatial domain decomposition based on block Jacobi algorithm for the diamond-difference scheme".  United States.  https://doi.org/10.1016/j.jcp.2015.05.033.  https://www.osti.gov/servlets/purl/1437429.

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@article{osti_1437429,

  title        = {Iterative stability analysis of spatial domain decomposition based on block Jacobi algorithm for the diamond-difference scheme},

  author       = {Anistratov, Dmitriy Y. and Azmy, Yousry Y.},

  abstractNote = {Here, we study convergence of the integral transport matrix method (ITMM) based on a parallel block Jacobi (PBJ) iterative strategy for solving particle transport problems. The ITMM is a spatial domain decomposition method proposed for massively parallel computations. AFourier analysis of the PBJ-based iterations applied to SN diamond-difference equations in 1D slab and 2D Cartesian geometries is performed. It is carried out for infinite-medium problems with homogeneous material properties. To analyze the performance of the ITMM with the PBJ algorithm and evaluate its potential in scalability we consider a limiting case of one spatial cell per subdomain. The analysis shows that in such limit the spectral radius of the iteration method is one without regard to values of the scattering ratio and optical thickness of the spatial cells. This implies lack of convergence in infinite medium. Numerical results of finite-medium problems are presented. They demonstrate effects of finite size of spatial domain on the performance of the iteration algorithm as well as its asymptotic behavior when the extent of the spatial domain increases. Finally, these numerical experiments also show that for finite domains iterative convergence to a finite criterion is achievable in a multiple of the sum of number of cells in each dimension.},

  doi          = {10.1016/j.jcp.2015.05.033},

  journal      = {Journal of Computational Physics},

  number       = C,

  volume       = 297,

  place        = {United States},

  year         = {Thu May 28 00:00:00 EDT 2015},

  month        = {Thu May 28 00:00:00 EDT 2015}

}

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Works referenced in this record:

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Wienke, B. R.; Hiromoto, R. E.
Transport Theory and Statistical Physics, Vol. 15, Issue 1-2
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Davidson, Gregory G.; Evans, Thomas M.; Jarrell, Joshua J.
Nuclear Science and Engineering, Vol. 177, Issue 2
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Properties of theS_N-Equivalent Integral Transport Operator in Slab Geometry and the Iterative Acceleration of Neutral Particle Transport Methods
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Title: Iterative stability analysis of spatial domain decomposition based on block Jacobi algorithm for the diamond-difference scheme

Abstract

Citation Formats

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journal, February 1986

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journal, April 1989

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journal, March 1998

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journal, March 2010

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journal, June 2014

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