网络机群下多项式预处理EBE-PCG并行算法设计与实现

DESIGN AND IMPLEMENTATION OF POLYNOMIAL-PRECONDITIONED EBE-PCG PARALLEL ALGORITHM IN CLUSTER

针对单机上实现困难，计算费用高昂的大规模结构动力学问题，本文采用将总体运算分解到单元上进行的EBE计算策略和基于区域分裂的SBS存储和任务分配策略，设计了粗粒度EBE－PCG并行算法，并在网络机群环境下得以实现。在PCG迭代法中分别采用Jacobi预处理矩阵和多项式预处理矩阵，比较它们的迭代求解效率。悬臂梁受冲击载荷与吉普车车架振动响应分析问题的数值算例，证明了该算法不但能够显著地提高问题的求解规模，适合大规模结构分析计算；而且还能获得良好的并行效率，是一种适合网络机群并行环境的有效的粗粒度并行算法。

The computation aiming at large-scale structural dynamic problems, which is difficult and expensive to be implemented on serial computers, has become more and more popular. Based on the EBE scheme disassembling global computation to local elements and the SBS scheme allocating storage and tasks to the subdomains plotted by domain decomposition, a coarse granular EBE-PCG parallel algorithm is designed and then implemented in cluster. Jacobi-preconditioned matrix and polynomial-preconditioned matrix are introduced in PCG iterative method and their efficiencies are compared. The numerical examples of the dynamic response analysis of jeep frame and cantilever beam show that the EBE-PCG algorithm can not only greatly enlarge the solution scale but also obtain high parallel efficiency. It is an efficient distributed coarse granular parallel algorithm suitable for large-scale structural analysis and computing in cluster.