Reducing Communication in Algebraic Multigrid Using Additive Variants

doi:10.1002/nla.1928

Title: Reducing Communication in Algebraic Multigrid Using Additive Variants

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Abstract

Algebraic multigrid (AMG) has proven to be an effective scalable solver on many high performance computers. However, its increasing communication complexity on coarser levels has shown to seriously impact its performance on computers with high communication cost. Moreover, additive AMG variants provide not only increased parallelism as well as decreased numbers of messages per cycle but also generally exhibit slower convergence. Here we present various new additive variants with convergence rates that are significantly improved compared to the classical additive algebraic multigrid method and investigate their potential for decreased communication, and improved communication-computation overlap, features that are essential for good performance on future exascale architectures.

Authors:

Vassilevski, Panayot S. ^[1]; Yang, Ulrike Meier ^[1]

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Publication Date:: 2014-02-12

Research Org.:: Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1237550

Report Number(s):: LLNL-JRNL-637872
Journal ID: ISSN 1070-5325

Grant/Contract Number:: AC52-07NA27344

Resource Type:: Journal Article: Accepted Manuscript

Journal Name:: Numerical Linear Algebra with Applications

Additional Journal Information:: Journal Volume: 21; Journal Issue: 1; Journal ID: ISSN 1070-5325

Publisher:: Wiley

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE

Citation Formats


                    Vassilevski, Panayot S., and Yang, Ulrike Meier. Reducing Communication in Algebraic Multigrid Using Additive Variants.  United States: N. p., 2014. 
        Web.  doi:10.1002/nla.1928.

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                    Vassilevski, Panayot S., & Yang, Ulrike Meier. Reducing Communication in Algebraic Multigrid Using Additive Variants.  United States.  doi:10.1002/nla.1928.

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                    Vassilevski, Panayot S., and Yang, Ulrike Meier. Wed .  
        "Reducing Communication in Algebraic Multigrid Using Additive Variants".  United States.  doi:10.1002/nla.1928.  https://www.osti.gov/servlets/purl/1237550.

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@article{osti_1237550,

  title        = {Reducing Communication in Algebraic Multigrid Using Additive Variants},

  author       = {Vassilevski, Panayot S. and Yang, Ulrike Meier},

  abstractNote = {Algebraic multigrid (AMG) has proven to be an effective scalable solver on many high performance computers. However, its increasing communication complexity on coarser levels has shown to seriously impact its performance on computers with high communication cost. Moreover, additive AMG variants provide not only increased parallelism as well as decreased numbers of messages per cycle but also generally exhibit slower convergence. Here we present various new additive variants with convergence rates that are significantly improved compared to the classical additive algebraic multigrid method and investigate their potential for decreased communication, and improved communication-computation overlap, features that are essential for good performance on future exascale architectures.},

  doi          = {10.1002/nla.1928},

  journal      = {Numerical Linear Algebra with Applications},

  issn         = {1070-5325},

  number       = 1,

  volume       = 21,

  place        = {United States},

  year         = {2014},

  month        = {2}

}

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DOI: 10.1002/nla.1928

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