SCALABILITY ANALYSIS OF PARALLEL GMRES IMPLEMENTATIONS

M. Sosonkina, D. Allison, L. Watson
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引用次数: 10

Abstract

Abstract Applications involving large sparse nonsymmetric linear systems encourage parallel implementations of robust iterative solution methods, such as GMRES(k). Two parallel versions of GMRES(k) based on different data distributions and using Householder reflections in the orthogonalization phase are analyzed with respect to scalability (their ability to maintain fixed efficiency with an increase in problem size and number of processors). A theoretical algorithm-machine model for scalability of GMRES(k) with fixed k is derived and validated by experiments on three parallel computers, each with different machine characteristics. The analysis for an adaptive version of GMRES(k), in which the restart value k is adapted to the problem, is also presented and scalability results for this case are briefly discussed.
并行gmres实现的可伸缩性分析
涉及大型稀疏非对称线性系统的应用鼓励并行实现鲁棒迭代求解方法,如GMRES(k)。基于不同数据分布并在正射化阶段使用Householder反射的两个并行版本的GMRES(k)在可伸缩性方面进行了分析(随着问题规模和处理器数量的增加,它们保持固定效率的能力)。推导了固定k时GMRES(k)可扩展性的理论算法-机器模型,并在三台具有不同机器特性的并行计算机上进行了实验验证。对GMRES(k)的自适应版本进行了分析,其中重新启动值k适合该问题,并简要讨论了该案例的可扩展性结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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