付朝江. 隐式非线性动力分析有限元并行求解格式[J]. 工程力学, 2010, 27(10): 27-033.
引用本文: 付朝江. 隐式非线性动力分析有限元并行求解格式[J]. 工程力学, 2010, 27(10): 27-033.
FU Chao-jiang. PARALLEL ALGORITHM FOR IMPLICIT NONLINEAR DYNAMIC FINITE ELEMENT ANALYSIS[J]. Engineering Mechanics, 2010, 27(10): 27-033.
Citation: FU Chao-jiang. PARALLEL ALGORITHM FOR IMPLICIT NONLINEAR DYNAMIC FINITE ELEMENT ANALYSIS[J]. Engineering Mechanics, 2010, 27(10): 27-033.

隐式非线性动力分析有限元并行求解格式

PARALLEL ALGORITHM FOR IMPLICIT NONLINEAR DYNAMIC FINITE ELEMENT ANALYSIS

  • 摘要: 针对非线性动力分析有限元并行计算,采取区域分解和预处理共轭梯度(PCG)算法,提出了三种并行求解格式。第一种整体界面格式(GIF)是将预处理共轭梯度算法应用于子区域组集的界面刚度系数矩阵;第二种局部界面格式(LIF)是利用子区域的非组集的局部Schur补矩阵构成预处理共轭梯度算法,采取不完全Cholesky预处理子;第三种局部子区域格式(LSF)是将预处理共轭梯度算法应用于局部非组集的子区域矩阵并且采用局部子区域信息构造预处理子。采用Newmark-β平均加速度法进行时间积分。编写了基于消息传递(MPI)编程模式的并行有限元程序。在工作站集群上实现了数值算例,分析了三种PCG格式的性能。计算结果表明提出的并行PCG格式优于传统的区域分解算法。

     

    Abstract: The three parallel algorithms for nonlinear dynamic analysis of large structures are presented using domain decomposition and preconditioned conjugate gradient (PCG) technique. In the first formulation called the global interface formulation, the PCG algorithm is applied on the assembled interface stiffness coefficient matrices of all subdomains. In the second formulation called local interface formulation, the PCG algorithm is formulated using the unassembled local Schur complement matrices of subdomains, where incomplete Cholesky preconditioner is employed. The third formulation called local subdomain formulation operates on the local unassembled subdomain matrices and the preconditioner is constructed using the local subdomain information. Newmark-β average acceleration technique is employed for time integration. A parallel program is developed with message passing interface as software development environment. Numerical example is implemented to validate as well as to evaluate the performance of the three proposed PCG formulations. Numerical studies indicate that the proposed parallel PCG formulations are superior in performance when compared to the conventional domain decomposition algorithms with parallel direct solver.

     

/

返回文章
返回