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

Iain Bethune*, J Mark Bull, Nicholas J. Dingle, Nicholas J. Higham

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)97-111
Number of pages15
JournalInternational Journal of High Performance Computing Applications
Issue number1
Early online date11 Jul 2013
Publication statusPublished - 1 Feb 2014


  • Asychronous algorithms
  • Jacobi
  • MPI
  • OpenMP
  • performance analysis
  • linear solvers
  • high performance computing


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