三维Poisson方程边值问题的块三对角可扩展并行算法  

A Scalable Parallel Algorithm of Block Tridiagonal Systems for the 3D-Poisson Equation Boundary Value Problem

作　　者：张衡[1,2] 张武[2] 苏变萍[3] 

机构地区：[1]石河子大学师范学院数学系,石河子832003 [2]上海大学计算机工程与科学学院,上海200072 [3]西安建筑科技大学理学院,西安710055

出　　处：《石河子大学学报（自然科学版）》2009年第4期518-521,共4页Journal of Shihezi University(Natural Science)

基　　金：教育部高等学校博士学科点专项科研基金项目(200802800007)

摘　　要：为探讨三维Poisson方程带Dirichlet边界条件边值问题的并行求解方法,本文使用块三对角可扩展并行算法对该系统进行求解,提出了反映差分格式内在并行性的概念——差分格式的并行度,利用此概念说了明差分格式自身内在并行性与并行算法性能的关系。此外,本文方法在上海大学"自强3000"计算机上的数值实验表明,实验的结果与理论分析一致;在保证精度的前提下得到了线性加速比,其并行效率达到90%以上。A scalable parallel algorithm of block tridiagonal systems for solving the boundary value problem of 3D- Poisson equation with the Dirichlet boundary condition is discussed. Parallel degree of the difference scheme is proposed for showing intrinsic parallelism of the difference scheme. The relation between the parallel degree and the performance of the parallel algorithm is investigated. The method proposed in this paper has been implemented on the super computer ＂ZiQiang 3000＂ of Shanghai University, and the numerical results match closely with theoretical analysis. With the given accuracy, the line speedup is obtained, and the parallel implementation efficiency over 90% is reached.

关 键 词：块三对角线性方程组 块对角占优 差分格式并行度 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]