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Iteration-fusing conjugate gradient for sparse linear systems with MPI + OmpSs

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Abstract

In this paper, we target the parallel solution of sparse linear systems via iterative Krylov subspace-based method enhanced with a block-Jacobi preconditioner on a cluster of multicore processors. In order to tackle large-scale problems, we develop task-parallel implementations of the preconditioned conjugate gradient method that improve the interoperability between the message-passing interface and OmpSs programming models. Specifically, we progressively integrate several communication-reduction and iteration-fusing strategies into the initial code, obtaining more efficient versions of the method. For all these implementations, we analyze the communication patterns and perform a comparative analysis of their performance and scalability on a cluster consisting of 32 nodes with 24 cores each. The experimental analysis shows that the techniques described in the paper outperform the classical method by a margin that varies between 6 and 48%, depending on the evaluation.

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Acknowledgements

This research was partially supported by the H2020 EU FETHPC Project 671602 “INTERTWinE.” The researchers from Universidad Jaume I were sponsored by Project TIN2017-82972-R of the Spanish Ministerio de Economía y Competitividad. Maria Barreda was supported by the POSDOC-A/2017/11 project from the Universitat Jaume I.

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Authors and Affiliations

  1. Dpto. de Ingeniería y Ciencia de Computadores, Universidad Jaime I, 12.071, Castellón, Spain

    María Barreda & José I. Aliaga

  2. Barcelona Supercomputing Center, 08034, Barcelona, Spain

    Vicenç Beltran & Marc Casas

Authors
  1. María Barreda
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  2. José I. Aliaga
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  3. Vicenç Beltran
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  4. Marc Casas
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Correspondence to María Barreda.

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Barreda, M., Aliaga, J.I., Beltran, V. et al. Iteration-fusing conjugate gradient for sparse linear systems with MPI + OmpSs. J Supercomput 76, 6669–6689 (2020). https://doi.org/10.1007/s11227-019-03100-4

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  • DOI: https://doi.org/10.1007/s11227-019-03100-4

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