Provably optimal parallel transport sweeps on regular grids

Michael P. Adams, Marvin L. Adams, W. Daryl Hawkins, Timmie Smith, Lawrence Rauchwerger, Nancy Marie Amato, Teresa S. Bailey, Robert D. Falgout

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We have found provably optimal algorithms for full-domain discrete-ordinate transport sweeps on regular grids in 3D Cartesian geometry. We describe these algorithms and sketch a "proof that they always execute the full eight-octant sweep in the minimum possible number of stages for a given P x × Py × Pz partitioning. Computational results demonstrate that our optimal scheduling algorithms execute sweeps in the minimum possible stage count. Observed parallel efficiencies agree well with our performance model. An older version of our PDT transport code achieves almost 80% parallel efficiency on 131,072 cores, on a weak-scaling problem with only one energy group, 80 directions, and 4096 cells/core. A newer version is less efficient at present-we are still improving its implementation - but achieves almost 60% parallel efficiency on 393,216 cores. These results conclusively demonstrate that sweeps can perform with high efficiency on core counts approaching 106.

Original languageEnglish (US)
Title of host publicationInternational Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2013
Pages2535-2553
Number of pages19
StatePublished - Sep 9 2013
Externally publishedYes
EventInternational Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2013 - Sun Valley, ID, United States
Duration: May 5 2013May 9 2013

Publication series

NameInternational Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2013
Volume4

Other

OtherInternational Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2013
CountryUnited States
CitySun Valley, ID
Period5/5/135/9/13

Keywords

  • PDT
  • Parallel transport
  • Performance models
  • STAPL
  • Transport sweeps

ASJC Scopus subject areas

  • Nuclear Energy and Engineering
  • Applied Mathematics

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  • Cite this

    Adams, M. P., Adams, M. L., Hawkins, W. D., Smith, T., Rauchwerger, L., Amato, N. M., Bailey, T. S., & Falgout, R. D. (2013). Provably optimal parallel transport sweeps on regular grids. In International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2013 (pp. 2535-2553). (International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2013; Vol. 4).