求解块三对角方程组的一种并行策略

Parallel strategy for solving block-tridiagonal linear systems

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HPrx2600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。

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.