research-article

On rounding error resilience, maximal attainable accuracy and parallel performance of the pipelined Conjugate Gradients method for large-scale linear systems in PETSc

Authors:

Siegfried Cools,

Emrullah Fatih Yetkin,

Emmanuel Agullo,

Luc GiraudAuthors Info & Claims

EASC '16: Proceedings of the Exascale Applications and Software Conference 2016

Article No.: 3, Pages 1 - 10

https://doi.org/10.1145/2938615.2938621

Published: 26 April 2016 Publication History

Abstract

Pipelined Krylov solvers typically display better strong scaling compared to standard Krylov methods for large linear systems. The synchronization bottleneck is mitigated by overlapping time-consuming global communications with computations. To achieve this hiding of communication, pipelined methods feature additional recurrence relations on auxiliary variables. This paper analyzes why rounding error effects have a significantly larger impact on the accuracy of pipelined algorithms. An algebraic model for the accumulation of rounding errors in the (pipelined) CG algorithm is derived. Furthermore, an automated residual replacement strategy is proposed to reduce the effect of rounding errors on the final solution. MPI parallel performance tests implemented in PETSc on an Intel Xeon X5660 cluster show that the pipelined CG method with automated residual replacement is more resilient to rounding errors while maintaining the efficient parallel performance obtained by pipelining.

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Cited By

Barreda MAliaga JBeltran VCasas M(2019)Iteration-fusing conjugate gradient for sparse linear systems with MPI + OmpSsThe Journal of Supercomputing10.1007/s11227-019-03100-4Online publication date: 10-Dec-2019
https://doi.org/10.1007/s11227-019-03100-4
Kestor GMutlu BManzano JSubasi OUnsal OKrishnamoorthy SKaeli DPericàs M(2018)Comparative analysis of soft-error detection strategiesProceedings of the 15th ACM International Conference on Computing Frontiers10.1145/3203217.3203240(173-182)Online publication date: 8-May-2018
https://dl.acm.org/doi/10.1145/3203217.3203240
Zhuang SCasas MGropp WBeckman PLi ZCazorla F(2017)Iteration-fusing conjugate gradientProceedings of the International Conference on Supercomputing10.1145/3079079.3079091(1-10)Online publication date: 14-Jun-2017
https://dl.acm.org/doi/10.1145/3079079.3079091
Show More Cited By

On rounding error resilience, maximal attainable accuracy and parallel performance of the pipelined Conjugate Gradients method for large-scale linear systems in PETSc
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms

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cover image ACM Other conferences

EASC '16: Proceedings of the Exascale Applications and Software Conference 2016

April 2016

59 pages

ISBN:9781450341226

DOI:10.1145/2938615

Copyright © 2016 ACM.

© 2016 Association for Computing Machinery. ACM acknowledges that this contribution was authored or co-authored by an employee, contractor or affiliate of a national government. As such, the Government retains a nonexclusive, royalty-free right to publish or reproduce this article, or to allow others to do so, for Government purposes only.

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SERC: SERC

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 26 April 2016

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Seventh Framework Programme

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EASC '16

EASC '16: Exascale Applications and Software Conference 2016

April 26 - 29, 2016

Stockholm, Sweden

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Cited By

Barreda MAliaga JBeltran VCasas M(2019)Iteration-fusing conjugate gradient for sparse linear systems with MPI + OmpSsThe Journal of Supercomputing10.1007/s11227-019-03100-4Online publication date: 10-Dec-2019
https://doi.org/10.1007/s11227-019-03100-4
Kestor GMutlu BManzano JSubasi OUnsal OKrishnamoorthy SKaeli DPericàs M(2018)Comparative analysis of soft-error detection strategiesProceedings of the 15th ACM International Conference on Computing Frontiers10.1145/3203217.3203240(173-182)Online publication date: 8-May-2018
https://dl.acm.org/doi/10.1145/3203217.3203240
Zhuang SCasas MGropp WBeckman PLi ZCazorla F(2017)Iteration-fusing conjugate gradientProceedings of the International Conference on Supercomputing10.1145/3079079.3079091(1-10)Online publication date: 14-Jun-2017
https://dl.acm.org/doi/10.1145/3079079.3079091
Scholl ABraun CWunderlich H(2017)Energy-efficient and error-resilient iterative solvers for approximate computing2017 IEEE 23rd International Symposium on On-Line Testing and Robust System Design (IOLTS)10.1109/IOLTS.2017.8046244(237-239)Online publication date: Jul-2017
https://doi.org/10.1109/IOLTS.2017.8046244
(2017)The communication-hiding pipelined BiCGstab method for the parallel solution of large unsymmetric linear systemsParallel Computing10.1016/j.parco.2017.04.00565:C(1-20)Online publication date: 1-Jul-2017
https://dl.acm.org/doi/10.1016/j.parco.2017.04.005

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