一类偏微分方程的几种并行迭代算法  

Parallel Iterative Algorithm of a Class of Differential Equations

作　　者：任铭[1,2] 张永胜[2] 景元萍[2] 

机构地区：[1]西北工业大学理学院,陕西西安710072 [2]洛阳理工学院数理部,河南洛阳471023

出　　处：《武汉理工大学学报（信息与管理工程版）》2011年第1期69-72,共4页Journal of Wuhan University of Technology：Information & Management Engineering

基　　金：河南省杰出青年基金资助项目(104100510018);河南省高校科技创新人才支持计划基金资助项目(2008HASTIT029);河南省教育厅科技攻关基金资助项目(2007520033)

摘　　要：许多工程和物理应用问题的求解通常都归结为求微分方程数值解,其核心是高效地求解线性方程组。基于单机性能不可能满足大规模科学与工程问题计算需求的考虑,针对一类偏微分方程,采用区域分解法给出了相应的并行差分格式,并在3种基本并行迭代求解算法的基础上提出了改进的红黑排序法和基于投影技术的并行算法,通过程序设计对这些迭代算法的加速比、并行效率等进行了分析,验证了算法具有良好的并行性和有效性。The solutions of many engineering and physical application questions are often ascribed to solve the numerical solution of the differential equations;the core of the method is to solve the linear equations efficiently.Based on that the single machine cannot be satisfied to compute the large-scale science and engineering questions,a parallel difference scheme with domain decomposition method was presented and the parallel iterative algorithm,which is the modified red-black ordering and parallel method based on projection technique,were proposed to a class of differential equations in this paper.Through programs design,the speedup ratio and parallel efficiency of these iterative algorithms had been analyzed scientifically,and it verified that they have excellent parallelism and validity.

关 键 词：红黑排序 共轭梯度法 多分裂迭代法 投影技术 

分 类 号：O175.2[理学—数学]