集群环境下复杂结构非线性动力有限元并行求解算法研究

Network parallel computing is a frontier subject of the numerical calculation research field at current.The computational complexities of nonlinear dynamic finite element analysis of complex structure may become very large for many practical engineering problems. It costs very long calculation time by using traditional serial finite element analysis.Parallel computing can remarkably reduce computing time.Exploring and developing the parallel algorithm with efficient characteristics of the parallel solution is imperative. The network parallel computing technology is used in the project.The mixed time integration parallel algorithm with concurrency for structural nonlinear dynamic analysis will be studied by integrating interface nodes with explicit time integration technique and solving local subdomains with implicit algorithm.The new parallel algorithm for nonlinear dynamic finite element analysis will be studied based on overlapped domain decomposition and clustering dynamic task allocation algorithm.The new parallel algorithms for structural nonlinear dynamic analysis will be studied.Namely,the PCG algorithm is applied on the unassembled interface stiffness coefficient matrices of all subdomains and incomplete Cholesky preconditioner is employed, and then the PCG algorithm is formulated using the unassembled local Schur complement matrices of subdomains.An elastic-plastic parallel algorithm is studied by substepping scheme and PCG method. A parallel program will be developed with message passing interface as software development environment.Numerical examples will be implemented to validate as well as to evaluate the performance of the proposed algorithm.The studies will provide new parallel algorithm for large-scale structural nonlinear dynamic analysis.

网络并行计算是当前数值计算研究领域的前沿课题，复杂结构的非线性动力有限元分析是一项计算密集型任务，传统的串行计算需要花费很长的计算时间。并行计算能显著减小结构分析时间，探讨和开发具有高效并行特性的并行求解算法势在必行。本项目采用网络并行计算技术，利用显式时间积分技术进行界面节点积分而隐式算法求解局部子区域，研究结构非线性动力反应的具有高效并发性的混合时间积分并行算法；基于重叠区域分解和群动态任务分配算法，研究基于重叠区域分解和群动态任务分配的新的并行算法；研究将PCG算法应用于子区域非组集的界面刚度系数矩阵、采取不完全Cholesky预处理子，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；研究子步法和PCG法相结合的弹塑性问题并行算法。开发基于消息传递编程模式的并行程序并在机群环境下实现工程结构问题的并行计算。本项目的研究将会为结构非线性动力分析提供新的高效并行算法。

网络并行计算是当前数值计算研究领域的前沿课题，结构非线性动力有限元分析是一项计算密集型任务，传统的串行计算需要花费很长的计算时间。并行计算能显著减小结构分析时间，研究和探讨具有高效并行特性的并行算法势在必行。本项目采用网络并行计算技术，利用显式时间积分技术进行界面节点积分而隐式算法求解局部子区域，研究了结构非线性动力反应的具有高效并发性的混合时间积分并行算法；基于重叠区域分解和群动态任务分配算法，研究了基于重叠区域分解和群动态任务分配的新的并行算法；基于子结构子空间迭代法，研究了结构特征值问题并行解法；将PCG算法应用于子区域非组集的界面刚度系数矩阵、采取不完全Cholesky预处理子，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，研究了新的并行求解格式；研究了子步法和PCG法相结合的弹塑性问题并行算法。基于消息传递界面，采取动态任务分配方法，利用计算与通信重叠，优化处理器间的通信，研究了高性能的并行算法；开展了工程结构动力作用的非线性动力分析研究，对具体结构算例的非线性动力问题进行了并行计算。经过本项目的研究，得到了结构非线性动力分析新的高效并行算法，切实推动并行计算的应用研究，实现结构非线性动力问题的快速有限元分析。