基于光滑聚集代数多重网格的有限元 并行计算实现方法

基于光滑聚集代数多重网格法实现一种用于结构有限元并行计算的预条件共轭梯度求解方法。对计算区域进行均匀划分，将这些子区域分配给各个进程同时进行单元刚度矩阵的计算，并组合形成分布式存储的整体平衡方程。采用光滑聚集代数多重网格预条件共轭梯度法对整体平衡方程进行并行求解，在天河二号超级计算机上进行数值试验,分析代数多重网格的主要参数对算法性能的影响，测试程序的并行计算性能。试验结果表明该方法具有较好的并行性能和可扩展性，适合于大规模实际应用。

Implementation of parallel finite element computation based on smoothed aggregation algebraic multi-grid

Based on the smoothed aggregation algebraic multi-grid, a preconditioned conjugate gradient method for parallel structural finite element computation is proposed. The structure is divided into substructures evenly, the substructures are assigned to processes to calculate the element stiffness matrix simultaneously, and the global equilibrium equations in the distributed storage are assembled. The parallel solution of the global equilibrium equations are improved by the smoothed algebraic multi-grid preconditioned conjugate gradient method. The numerical test is carried out on the Tianhe 2 super computer. The influence of the main parameters of algebraic multi-grid on the algorithm performance is analyzed, and the parallel computation performance of the process is assessed. The numerical results show that the proposed implementation is of good parallel performance and scalability, and it can be used in large-scale applications.