基于残余平滑-预处理共轭梯度算法的有限元并行计算

发布时间：2018-10-13 11:23

【摘要】：针对弹塑性问题的有限元分析非常耗时,基于消息传递接口(MPI)集群环境,提出了残余平滑的子结构预处理共轭梯度并行算法。采取区域分解,将子结构通过界面条件处理为独立的有限元模型。整体分析时,每个处理器仅存储与其相关的子结构信息并生成局部刚度矩阵。采用对角存储方式和最小残余平滑法,设计出了结合残余平滑(MR)的并行子结构预处理共轭梯度(PCG)算法。并行算法中对负载平衡进行了探讨,对处理器间的通信进行了优化。利用子步法对弹塑性应力应变进行积分,根据预定的容许值自动调整每个子步的大小来控制积分过程的误差。在工作站集群上实现了数值算例,分析了算法的性能,计算性能与传统的PCG算法进行了比较。算例显示:所提算法具有良好的加速比和效率,优于传统的PCG算法,对弹塑性问题的有限元分析,是一种有效的并行求解算法。
[Abstract]:The finite element analysis of elastoplastic problems is time-consuming. Based on the (MPI) cluster environment of message passing interface, a substructure preprocessing conjugate gradient parallel algorithm is proposed. The substructure is treated as an independent finite element model through interfacial conditions by domain decomposition. In global analysis, each processor only stores the substructure information associated with it and generates a local stiffness matrix. Using diagonal storage method and minimal residual smoothing method, a parallel substructure preconditioned conjugate gradient (PCG) algorithm combined with residual smooth (MR) is designed. Load balancing is discussed in parallel algorithm and communication between processors is optimized. The elastic-plastic stress-strain integration is carried out by substep method and the error of the integration process is controlled automatically by adjusting the size of each sub-step according to the predetermined allowable value. A numerical example is implemented on a workstation cluster. The performance of the algorithm is analyzed and compared with the traditional PCG algorithm. Numerical examples show that the proposed algorithm has a good speedup and efficiency, and is superior to the traditional PCG algorithm. The finite element analysis of elastic-plastic problems is an effective parallel algorithm.
【作者单位】：福建工程学院土木工程学院;福建省土木工程新技术与信息化重点实验室;
【基金】：国家自然科学基金资助项目(51378124)
【分类号】：TP338.6

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