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Modeling 1D Distributed-Memory Dense Kernels for an Asynchronous Multifrontal Sparse Solver

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High Performance Computing for Computational Science -- VECPAR 2014 (VECPAR 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8969))

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Abstract

To solve sparse systems of linear equations, multifrontal methods rely on dense partial \(LU\) decompositions of so-called frontal matrices; we consider a parallel asynchronous setting in which several frontal matrices can be factored simultaneously. In this context, to address performance and scalability issues of acyclic pipelined asynchronous factorization kernels, we study models to revisit properties of left and right-looking variants of partial \(LU\) decompositions, study the use of several levels of blocking, before focusing on communication issues. The general purpose sparse solver MUMPS has been modified to implement the proposed algorithms and confirm the properties demonstrated by the models.

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Notes

  1. 1.

    http://www.netlib.org/hpl/.

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Acknowledgement

This work was granted access to the HPC resources of CALMIP under the allocation 2013-0989 and GENCI/IDRIS resources under allocation x2013065063.

Author information

Authors and Affiliations

  1. University of Toulouse, INPT(ENSEEIHT)-IRIT, Toulouse, France

    Patrick R. Amestoy

  2. University of Lyon, Inria and LIP (CNRS, ENS Lyon, Inria, UCBL), Lyon, France

    Jean-Yves L’Excellent

  3. Lawrence Berkeley National Laboratory, Berkeley, USA

    François-Henry Rouet

  4. University of Lyon, ENS Lyon and LIP (CNRS, ENS Lyon, Inria, UCBL), Lyon, France

    Wissam M. Sid-Lakhdar

Authors
  1. Patrick R. Amestoy
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  2. Jean-Yves L’Excellent
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  3. François-Henry Rouet
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  4. Wissam M. Sid-Lakhdar
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Corresponding author

Correspondence to Wissam M. Sid-Lakhdar .

Editor information

Editors and Affiliations

  1. IRIT, ENSEEIHT, Toulouse Cedex, France

    Michel Daydé

  2. Lawrence Berkeley National Laboratory, Berkeley, California, USA

    Osni Marques

  3. Information Technology Center, The University of Tokyo, Tokyo, Japan

    Kengo Nakajima

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Amestoy, P.R., L’Excellent, JY., Rouet, FH., Sid-Lakhdar, W.M. (2015). Modeling 1D Distributed-Memory Dense Kernels for an Asynchronous Multifrontal Sparse Solver. In: Daydé, M., Marques, O., Nakajima, K. (eds) High Performance Computing for Computational Science -- VECPAR 2014. VECPAR 2014. Lecture Notes in Computer Science(), vol 8969. Springer, Cham. https://doi.org/10.1007/978-3-319-17353-5_14

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  • DOI: https://doi.org/10.1007/978-3-319-17353-5_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-17352-8

  • Online ISBN: 978-3-319-17353-5

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