改进的并行广义共轭残差算法

Improved Parallel Generalized Conjugate Residual Algorithm

针对大型非对称稀疏线性方程组的求解,通过利用广义共轭残差(GCR)算法的固有性质,消除GCR算法的内积计算数据相关性,给出一种改进的广义共轭残差(IGCR)算法。IGCR算法与GCR算法有相同的收敛性,在基于MPI的分布式存储并行机群上进行并行计算时,同步开销次数减少为GCR算法的一半。数值计算结果与理论分析表明,IGCR算法的性能优于GCR算法。

By relying on an intrinsic property of the Generalized Conjugate Residual（GCR） algorithm and eliminating data interdependence for inner product computation in the GCR algorithm, an improved parallel GCR algorithm is proposed for solving large non-symmetric sparse linear systems in this paper. The convergence of IGCR algorithm is the same as GCR algorithm, but the times of the synchronization overhead are reduced by a factor of two when it computes using the IGCR algorithm on distributed memory cluster systems based on MPI environment. The numerical result and theoretical analysis prove that the performance of the IGCR algorithm is better than that of the GCR algorithm.