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

Ever-increasing core counts create the need to develop parallel algorithms that avoid closely coupled execution across all cores. We present performance analysis of several parallel asynchronous implementations of Jacobi’s method for solving systems of linear equations, using MPI, SHMEM and OpenMP....

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Bibliographic Details
Published in:The international journal of high performance computing applications 2014-02, Vol.28 (1), p.97-111
Main Authors: Bethune, Iain, Bull, J Mark, Dingle, Nicholas J, Higham, Nicholas J
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Asynchronous
Computer science
control theory
systems
Computer systems and distributed systems. User interface
Exact sciences and technology
Linear equations
Mathematical problems
Programming languages
Software
Studies
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Summary:Ever-increasing core counts create the need to develop parallel algorithms that avoid closely coupled execution across all cores. 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, discuss how our specific implementations could be generalised to other classes of problem, and suggest how existing parallel programming models might be extended to allow asynchronous algorithms to be expressed more easily.
ISSN:1094-3420
1741-2846
DOI:10.1177/1094342013493123