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(英文)

Parallel version of generalized product-type bi-conjugate residual method suitable for distributed parallel computing

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.

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%.