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    Segmental Refinement: A Multigrid Technique for Data Locality

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    Type
    Article
    Authors
    Adams, Mark F.
    Brown, Jed
    Knepley, Matt
    Samtaney, Ravi cc
    KAUST Department
    Fluid and Plasma Simulation Group (FPS)
    Mechanical Engineering Program
    Physical Science and Engineering (PSE) Division
    Date
    2016-08-04
    Online Publication Date
    2016-08-04
    Print Publication Date
    2016-01
    Permanent link to this record
    http://hdl.handle.net/10754/621908
    
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    Abstract
    We investigate a domain decomposed multigrid technique, termed segmental refinement, for solving general nonlinear elliptic boundary value problems. We extend the method first proposed in 1994 by analytically and experimentally investigating its complexity. We confirm that communication of traditional parallel multigrid is eliminated on fine grids, with modest amounts of extra work and storage, while maintaining the asymptotic exactness of full multigrid. We observe an accuracy dependence on the segmental refinement subdomain size, which was not considered in the original analysis. We present a communication complexity analysis that quantifies the communication costs ameliorated by segmental refinement and report performance results with up to 64K cores on a Cray XC30.
    Citation
    Adams MF, Brown J, Knepley M, Samtaney R (2016) Segmental Refinement: A Multigrid Technique for Data Locality. SIAM Journal on Scientific Computing 38: C426–C440. Available: http://dx.doi.org/10.1137/140975127.
    Sponsors
    This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, and performed under the auspices of the U.S. Department of Energy by Lawrence Berkeley National Laboratory under contract DE-AC02-05CH11231. This research used resources of the National Energy Research Scientific Computing Center, which is a DOE Office of Science User Facility. Authors from Lawrence Berkeley National Laboratory were supported by the U.S. Department of Energy's Advanced Scientific Computing Research Program under contract DEAC02-05CH11231.
    Publisher
    Society for Industrial & Applied Mathematics (SIAM)
    Journal
    SIAM Journal on Scientific Computing
    DOI
    10.1137/140975127
    arXiv
    1406.7808
    Additional Links
    http://epubs.siam.org/doi/10.1137/140975127
    ae974a485f413a2113503eed53cd6c53
    10.1137/140975127
    Scopus Count
    Collections
    Articles; Physical Science and Engineering (PSE) Division; Mechanical Engineering Program

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