三角形方程组的一种分布式并行算法

A Parallel Algorithm for Solving Triangular Equations Under Distributed Memory Environments

本文提出了一种在分布式存储环境下求解三角形方程组的并行算法,该算法将系数矩阵及右端项以行卷帘方式分布存储到各处理机中。算法中引入了一个一维p阶向量F,该向量的循环传送使处理机间的通信次数明显下降,同时该算法还采用了计算与通信重叠的技术。理论分析与数值实验表明,该算法较列扫描并行算法优越。

A new parallel algorithm for solving triangular systems under distributed-memory environments is presented in this paper. The triangular matrix and its right hand sides are distributed among all processors through row torus-wrap mapping. In this algorithm, a vector F is introduced which has p elements. The times of communication are decreased by conveying the vector F among all of the processors. Meanwhile, this algorithm adopts the technology of overlapping computation and communication. The theoretical analysis and numerical experiment show that the new algorithm is better than the line-scan algorithm.