Performance analysis of asynchronous Jacobi's method implemented in MPI, SHMEM and OpenMP

Bethune, Iain and Bull, J. Mark and Dingle, Nicholas J. and Higham, Nicholas J. (2012) Performance analysis of asynchronous Jacobi's method implemented in MPI, SHMEM and OpenMP. [MIMS Preprint]

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Abstract

Ever-increasing core counts create the need to develop parallel algorithms that avoid closely- coupled execution across all cores. In this paper we present performance analysis of several parallel asynchronous implementations of Jacobi's method for solving systems of linear equations, using MPI, SHMEM and OpenMP. In particular we have solved systems of over 4 billion unknowns using up to 32,768 processes on a Cray XE6 supercomputer. We show that the precise implementation details of asynchronous algorithms can strongly affect the resulting performance and convergence behaviour of our solvers in unexpected ways.

Item Type: MIMS Preprint
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory
MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
MSC 2010, the AMS's Mathematics Subject Classification > 68 Computer science
Depositing User: Dr Nicholas Dingle
Date Deposited: 15 Jun 2012
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1838

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