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A 2D algorithm with asymmetric workload for the UPC conjugate gradient method

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Abstract

This paper examines four different strategies, each one with its own data distribution, for implementing the parallel conjugate gradient (CG) method and how they impact communication and overall performance. Firstly, typical 1D and 2D distributions of the matrix involved in CG computations are considered. Then, a new 2D version of the CG method with asymmetric workload, based on leaving some threads idle during part of the computation to reduce communication, is proposed. The four strategies are independent of sparse storage schemes and are implemented using Unified Parallel C (UPC), a Partitioned Global Address Space (PGAS) language. The strategies are evaluated on two different platforms through a set of matrices that exhibit distinct sparse patterns, demonstrating that our asymmetric proposal outperforms the others except for one matrix on one platform.

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Notes

  1. For practical purposes, the algorithm is often used with preconditioners but this is not in the scope of this paper.

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Acknowledgments

This work was funded by the Ministry of Economy and Competitiveness of Spain and FEDER funds of the EU (Project TIN2013-42148-P), by the Galician Government (Consolidation Program of Competitive Reference Groups GRC2013/055) and by the U.S. Department of Energy (Contract No. DE-AC03-76SF00098).

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Authors and Affiliations

  1. Parallel and Distributed Architectures Group, Johannes Gutenberg University-Mainz, Mainz, Germany

    Jorge González-Domínguez

  2. Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Osni A. Marques

  3. Computer Architecture Group, University of A Coruña, A Coruña, Spain

    María J. Martín & Juan Touriño

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  1. Jorge González-Domínguez
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  2. Osni A. Marques
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  3. María J. Martín
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  4. Juan Touriño
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Correspondence to Jorge González-Domínguez.

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González-Domínguez, J., Marques, O.A., Martín, M.J. et al. A 2D algorithm with asymmetric workload for the UPC conjugate gradient method. J Supercomput 70, 816–829 (2014). https://doi.org/10.1007/s11227-014-1300-0

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