初边值问题的块三对角可扩展并行算法

上海大学学报(自然科学版) ›› 2007, Vol. 13 ›› Issue (5): 497-503 .

初边值问题的块三对角可扩展并行算法

张武1，张衡1，2

1.上海大学计算机工程与科学学院，上海 200072； 2.石河子大学数学系，石河子 832000

收稿日期:2007-05-10 修回日期:1900-01-01 出版日期:2007-10-20 发布日期:2007-10-20
通讯作者: 张武1

Scalable Parallel Algorithm of Block Tridiagonal Systems
for Initial Boundary Value Problem

ZHANG Wu1,ZHANG Heng1,2

1. School of Computer Engineering and Science, Shanghai University, Shanghai 200072, China;
2. Department of Mathematics, Shihezi University, Shihezi 832000, China

Received:2007-05-10 Revised:1900-01-01 Online:2007-10-20 Published:2007-10-20
Contact: ZHANG Wu1

摘要/Abstract

摘要： 该文对二维抛物型方程带Dirichlet边界条件初边值问题的离散系统使用块三对角可扩展并行算法求解.提出反映差分格式内在并行性的概念——差分格式的并行度，利用这个概念说明差分格式自身内在并行性对并行算法性能的影响.使用该方法在上海大学超级计算机“自强3000”上进行了数值实验，实验结果与理论分析一致.在保证精度的前提下，得到线性加速比，并行效率达到90%以上.

关键词: 并行度, 矩阵分割, 块对角占优, 块三对角线性方程组

Abstract: A scalable parallel algorithm of block tridiagonal systems is discussed to solve initial boundary value problems of 2D-parabolic equation with the Dirichlet boundary condition. A parallel degree of the difference scheme is proposed to show the intrinsic parallelism of the difference scheme. The relation between the parallel degree and the performance of the parallel algorithm is investigated. The proposed method has been implemented on the supercomputer “ZiQiang 3000” of Shanghai University. The numerical results closely match the theoretical analysis. At given accuracy, the linear speedup rate is obtained, and parallel efficiency over 90% is reached.

Key words: block diagonal dominant, matrix partitioning, parallel degree, block tridiagonal systems

张武;张衡;. 初边值问题的块三对角可扩展并行算法[J]. 上海大学学报(自然科学版), 2007, 13(5): 497-503 .

ZHANG Wu;ZHANG Heng;. Scalable Parallel Algorithm of Block Tridiagonal Systems
for Initial Boundary Value Problem [J]. Journal of Shanghai University（Natural Science Edition）, 2007, 13(5): 497-503 .