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适合于分布式并行计算的一种并行广义乘积型双共轭残差方法
  • ISSN号：1006-6330
  • 期刊名称：应用数学与计算数学学报
  • 时间：2013.6.1
  • 页码：-
  • 分类：O246[理学—计算数学;理学—数学] O241.6[理学—计算数学;理学—数学]
  • 作者机构：[1]河南大学计算机与信息工程学院,河南开封475004, [2]北京应用物理与计算数学研究所计算物理实验室,北京100088, [3]北京应用物理与计算数学研究所高性能计算中心,北京100088
  • 相关基金：Project is supported by the National Natural Science Foundation of China （61170309; 61202098 91130024）, the Key Project of Development Foundation of Science and Technology of CAEP （2011A0202012 2012A0202008）, and the Foundation of National Key Laboratory of Computational Physics
  • 相关项目：异构多核并行机上线性代数方程组的快速算法研究
作者： 左宪禹|谷同祥|莫则尧|刘兴平|
关键词： 稀疏非对称线性方程组, 并行广义乘积型双共轭残差方法, KRYLOV子空间方法, 全局通讯, 分布式并行环境, sparse unsymmetrical linear systems, parallel version of generalized product-type bi-conjugate residual （PGPBiCR） method, Krylov subspace method, global communication, distributed parallel environment
中文摘要：

针对求解大型稀疏非对称线性方程组, 提出适合于分布式并行环境的一种并行广义乘积型双共轭残差 （GPBiCR） 方法 （简记为PGPBiCR方法）. 通过重构GPBiCR方法, 新方法将原方法中的三个全局同步点降低到了一个, 且内积所需的通讯时间可与向量校正的计算时间有效地重叠. 代价仅是稍微增加了一些计算量, 而相比于全局通讯时间的降低, 这是可以忽略不计的. 性能和等效率分析表明, PGPBiCR方法比GPBiCR方法具有更好的并行性和可扩展性, 其中可扩展性可改进3倍, 而并行通讯性能可改进66.7%. 数值试验得到了与理论分析相吻合的结果.

英文摘要：

A parallel version of generalized product-type bi-conjugate residual （GPBiCR） method （PGPBiCR method, in brief） for solving large sparse linear systems with unsymmetrical coefficient matrices is proposed for distributed parallel environments. The method reduces three global synchronization points to one by reconstructing the GPBiCR method, and the communication time required for the inner product can be efficiently overlapped with the computation time of the vector updates. The cost is only slightly increased count of computation, which can be ignored, compared with the reduction of the communication time. Performance and isoefficiency analysis show that the PGPBiCR method has better parallelism and scalability than the GPBiCR method. Numerical experiments show that the scalability can be improved by a factor 3 and the improvement in parallel communication performance approaches 66.7%.

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期刊信息
  • 《应用数学与计算数学学报》
  • 主管单位:上海市教育委员会
  • 主办单位:上海大学
  • 主编：马和平
  • 地址：上海市上大路99号121信箱上海大学期刊社
  • 邮编：200444
  • 邮箱：camc@oa.shu.edu.cn
  • 电话：021-66137602
  • 国际标准刊号：ISSN：1006-6330
  • 国内统一刊号：ISSN：31-1436/O1
  • 邮发代号:
  • 获奖情况:
  • 国内外数据库收录:
  • 美国数学评论（网络版）,德国数学文摘
  • 被引量:1282