大型结构特征值问题的混合粒度并行算法

本文提出一种求解大形结构特征值问题的粗细粒度混合并行算法：在子结构模态综合粗粒度并行算基础上，综合系统的特性值问题采用细粒度并行方式求解。细粒度并行包括子空间迭代法的子结构并行算法、雅可比分块并行计算的方法和一种Ｎｅｗｔｏｎ－Ｒａｐｈｏｎ迭代法在多处理器上任力均衡分配的有效策略。子空间迭代法的子结构并行计算的实施是利用子结构的刚度阵和质量阵而不必完全组集系统刚度阵和国求综合系统的特征值问题。利用雅

A Hybrid Granularity Parallel Algorithm to Solve the Large Structure Eigenproblem

In this paper, large - scale structural eigenproblem is discussed. On the basis of mode synthesis, the eigenproblem of integrated system is solved combing subspace iterative method and improved Newton - Raphon iterative method, which is time saving compared with the solution using subspace iterative method only. Then, a hybrid granularity parallel algorithm to solve large - scale 'structural eigenproblem is presented, that is , on the basis of coarse granularity parallelization of substructure mode synthesis, the eigenproblem of integrated system is solved using fine granularity parallel method. The fine granularity parallel method includes substructure subspace iterative method, the Jacobi sub - block parallel algorithm and task distributing strategy on multiprocessors of Newton - Raphon iterative method. The substructure subspace iterative method is implemented using the stiff matrix and mass matrix of substructures without assembling the stiff and mass matrix of whole system. Considering the special properties of Jacobi method, the sub - blocks with every element in it whose row and column are not the same with other sub - blocks can be processed using Jacobi method concurrendy. To keep the task balance of each processor, a task allocating strategy of Newton -Raphon iterative method is given considering the precision of the initial iterative eigenpairs. The numerical results show that this hybrid parallel algorithm is effective for large structure eigenproblem.