双CPU并行算法求解Poisson方程零边界值问题试验

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Numerical Experiments of Poisson Equation Zero-Boundary with Dual-CPU Parallel Algorithm

摘要: 本文是把传统的大气、海洋问题中常用的串行迭代法——Liebmann方法（点迭代）和局地格林函数迭代法（局地点迭代），从算法上变成适合于IBM—4381（P03）双CPU并行执行的并行算法，求解Poisson方程零边界值问题。实例计算试验表明：上述两种方法的并行算法的效率是同一计算问题的串行算法的1.8倍和1.9倍；若把区域扩大，局地格林函数并行迭代效率可达2.8倍，大大超过IBM公司所称P03型机是P01型机的1.7倍的效率；本文还指出IBM-4381（P03）型计算机的两个CPU在执行并行运算时，可以共享数据组。

Abstract: In this paper, Liebmann method (point iterative) and Local Green Function method (local point iterative) which are usually used in traditional atmospheric/oceanic calculating problems are modified to parallel algorithms adapting to the dual-CPU in IBM-4381 (P03) to solve the Poisson equation for zero-boundary value. The numerical experimental results show that the calculation speed of parallel algorithm is 1.8 or 1.9 times as much as serial algorithm for the same calculating problems. However, when expanding the areas, parallel iterative speed of Local Green Function can reach 2.8 time which exceeds the best speedup (1.7 times for P01) declared by IBM Company. The paper also points out that the data array can be shared by the IBM-4381 (P03) CPU when running parallel calculations