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Provably optimal parallel transport sweeps on semi-structured grids

Journal Article · · Journal of Computational Physics
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  1. Texas A & M Univ., College Station, TX (United States)
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
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We have found provably optimal algorithms for full-domain discrete-ordinate transport sweeps on a class of grids in 2D and 3D Cartesian geometry that are regular at a coarse level but arbitrary within the coarse blocks. We describe these algorithms and show that they always execute the full eight-octant (or four-quadrant if 2D) sweep in the minimum possible number of stages for a given Px x Py x Pz partitioning. Computational results confirm that our optimal scheduling algorithms execute sweeps in the minimum possible stage count. Observed parallel efficiencies agree well with our performance model. Our PDT transport code has achieved approximately 68% parallel efficiency with > 1.5M parallel threads, relative to 8 threads, on a simple weak-scaling problem with only three energy groups, 10 directions per octant, and 4096 cells/thread. Our ARDRA code has achieved 71% efficiency with < 1.5M cores, relative to 16 cores, with 36 directions per octant and 48 energy groups. We demonstrate similar efficiencies with PDT on a realistic set of nuclear-reactor test problems, with unstructured meshes that resolve fine geometric details. These results demonstrate that discrete-ordinates transport sweeps can be executed with high efficiency using more than 106 parallel processes.
Research Organization:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Organization:
USDOE; USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC)
Grant/Contract Number:
AC02-06CH11357; AC52-07NA27344; FC52-08NA28616; NA0002376
OSTI ID:
1869515
Alternate ID(s):
OSTI ID: 1701937
Report Number(s):
LLNL-JRNL-815552; 1022085
Journal Information:
Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: N/A Vol. 407; ISSN 0021-9991
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English

References (7)

The STAPL parallel container framework journal February 2011
Fast iterative methods for discrete-ordinates particle transport calculations journal January 2002
A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids journal April 2008
An Algorithm for Parallel S n Sweeps on Unstructured Meshes journal February 2002
Concurrent Source Iteration in the Solution of Three-Dimensional, Multigroup Discrete Ordinates Neutron Transport Equations journal March 1996
An S n Algorithm for the Massively Parallel CM-200 Computer journal March 1998
Denovo: A New Three-Dimensional Parallel Discrete Ordinates Code in SCALE journal August 2010

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Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
97 MATHEMATICS AND COMPUTING
STAPL
parallel algorithms
parallel transport sweeps
performance model
s unstructured mesh
scheduling algorithms