Pipelined Preconditioned s-step Conjugate Gradient Methods for Distributed Memory Systems

Tiwari, M and Vadhiyar, S (2021) Pipelined Preconditioned s-step Conjugate Gradient Methods for Distributed Memory Systems. In: 2021 IEEE International Conference on Cluster Computing, Cluster 2021, 7-10 Sep 2021, Portland, OR, USA (Virtual), pp. 215-225.

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Abstract

Preconditioned Conjugate Gradient (PCG) method is a widely used iterative method for solving large linear systems of equations. Pipelined variants of PCG present independent computations in the PCG method and overlap these computations with non-blocking allreduces. We have developed a novel pipelined PCG algorithm called PIPE-sCG (Pipelined s-step Conjugate Gradient) that provides a large overlap of global communication and computations at higher number of cores in distributed memory CPU systems. Our method achieves this overlap by introducing new recurrence computations. We have also developed a preconditioned version of PIPE-sCG. The advantages of our methods are that they do not introduce any extra preconditioner or sparse matrix vector product kernels in order to provide the overlap and can work with preconditioned, unpreconditioned and natural norms of the residual, as opposed to the state-of-the-art methods. We compare our method with other pipelined CG methods for Poisson problems and demonstrate that our method gives the least runtimes. Our method gives up to 2.9x speedup over PCG method, 2.15x speedup over PIPECG method and 1.2x speedup over PIPECG-OATI method at large number of cores. ©2021 IEEE.

Item Type:	Conference Paper
Publication:	Proceedings - IEEE International Conference on Cluster Computing, ICCC
Publisher:	Institute of Electrical and Electronics Engineers Inc.
Additional Information:	The copyright for this article belongs to Institute of Electrical and Electronics Engineers Inc.
Keywords:	Linear systems; Memory architecture; Pipelines, Conjugate-gradient method; Distributed memory systems; Linear systems of equations; Non-blocking; Overlapping communication and computations; Pipelining; Preconditioned conjugate gradient; Preconditioned conjugate gradient method; S-step method; Step method, Conjugate gradient method
Department/Centre:	Division of Interdisciplinary Sciences > Computational and Data Sciences
Date Deposited:	15 May 2022 17:59
Last Modified:	15 May 2022 17:59
URI:	https://eprints.iisc.ac.in/id/eprint/71666

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