并行GCR(k)算法在多尺度预报模式中的应用

摘要

Employing an intrinsic propcrty of the GCR (k) algodthm and eliminating data interdependence for inner product computation in the GCR (k) algorithm, an improved parallel GCR (k) algorithm called IGCR (k) algorithm is established for solving large non-symmetric sparse linear systems derived from multi-scale prediction model. The convergence of IGCR (k) algorithm is as same as GCR (k) algorithm, but the times of the synchronization overhead arc reduced by a factor of two when we compute using the IGCR (k) algorithm on distributed memory cluster systems based on MPI environment. The numerical result and theoretical analysis prove that the performance of the IGCR (k) algorithm is better than that of the GCR (k) algorithm.%针对多尺度预报模式离散得到的非对称稀疏线性方程组的求解,通过利用GCR(k)算法的固有性质,消除GCR(k)算法的内积计算数据相关性,给出了一种改进的GCR(R)(IGCR(k))算法.同GCR(k)算法对比,IGCR(k)算法与GCR(k)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(k)算法的一半.数值计算结果与理论分析表明改进的GCR(k)算法的性能要优于GCR(k)算法.