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

机译:MPI,SHMEM和OpenMP中实现的异步Jacobi方法的性能分析

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摘要

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.
机译:不断增加的内核数量导致需要开发并行算法,从而避免所有内核之间紧​​密耦合的执行。我们介绍了使用MPI,SHMEM和OpenMP求解Jacobi方法求解线性方程组的方法的几种并行异步实现的性能分析。特别是,我们在Cray XE6超级计算机上使用多达32,768个进程解决了超过40亿个未知数的系统。我们展示了异步算法的精确实现细节会以意想不到的方式极大地影响求解器的性能和收敛行为,讨论如何将我们的特定实现推广到其他类别的问题,并建议如何扩展现有的并行编程模型以便更轻松地表达异步算法。

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