Parallel strategy for solving block-tridiagonal linear systems

Computer Engineering and Applications ›› 2011, Vol. 47 ›› Issue (13): 46-49.

• 研究、探讨 • Previous Articles Next Articles

Parallel strategy for solving block-tridiagonal linear systems

DUAN Zhijian1，YANG Yong1，LV Quanyi2，MA Xinrong3

1.National Key Lab of Aerodynamic Design and Research，Northwestern Polytechnical University，Xi’an 710072，China
2.Department of Applied Mathematics，Northwestern Polytechnical University，Xi’an 710072，China
3.Department of Mathematics，Xianyang Normal University，Xianyang，Shaanxi 712000，China

Received:1900-01-01 Revised:1900-01-01 Online:2011-05-01 Published:2011-05-01

求解块三对角方程组的一种并行策略

段治健1，杨永1，吕全义2，马欣荣3

1.西北工业大学翼型叶栅空气动力学国防科技重点实验室，西安 710072
2.西北工业大学应用数学系，西安 710072
3.咸阳师范学院数学系，陕西咸阳 712000

Abstract

Abstract: This paper focuses on a parallel iterative method for solving block-tridiagonal linear systems on distributed-memory multi-computers.Through choosing the base of subspace based on Galerkin theory，the communication only need twice between the adjacent processors per iteration step.Furthermore，the sufficient condition for convergence is given when the coefficient matrix A is a symmetric positive definite matrix.Finally，the numerical experiments implemented on HP rx2600 cluster indicate that the algorithm’s parallel acceleration rates and efficiency are higher than the multi-splitting method’s.

Key words: block-tridiagonal linear systems, Galerkin theory, HP rx2600 cluster, parallelism

摘要： 提出了一种在MIMD分布式存储环境下求解块三对角线性方程组的并行算法。基于Galerkin原理适当取基构造算法，使整个计算过程只在相邻处理机间通信两次，并给出了系数矩阵为对称正定矩阵时算法收敛的条件。在HP rx2600集群系统上进行的数值计算结果表明该算法与多分裂方法相比具有较高的加速比和并行效率。

关键词: 块三对角线性方程组, Galerkin原理, HP rx2600集群, 并行性

DUAN Zhijian1，YANG Yong1，LV Quanyi2，MA Xinrong3. Parallel strategy for solving block-tridiagonal linear systems[J]. Computer Engineering and Applications, 2011, 47(13): 46-49.

段治健1，杨永1，吕全义2，马欣荣3. 求解块三对角方程组的一种并行策略[J]. 计算机工程与应用, 2011, 47(13): 46-49.

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Parallel strategy for solving block-tridiagonal linear systems

求解块三对角方程组的一种并行策略

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