关键词: 并行算法, 多项式割线迭代法, 矢量逆迭代法

Abstract: In this paper, a parallel algorithm of structural natural frequencies and vibrating modes is presented by using the polynomial secant iterative method and inverse power method. The method first utilizes the polynomial secant iterative method to determine the approximate value of every eigenvalue and introduces the parallel step. Then these eigenvalues are classified into N regions(N is the number of CPU). The shift parameters are taken as the central values of these regions. Finally, the inverse power method is used to get the exact eigenvalues and eigenvectors in the neighborhood of shift parameters concurrently in every CPU by introducing every shift parameter. The program of these algorithm has been realized on the ELXSI-6400 parallel computer of Xian Jiaotong University. The computational results show the CPU times can be saved effectively, and the algorithm is effective in the dynamic analysis of larg-scale engineering structures.

Key words: parallel algorithm, polynomial secant iterative method, inverse power method