Parallel computing study for the large-scale generalized eigenvalue problems in modal analysis

In this paper we study the algorithms and their parallel implementation for solving large-scale generalized eigenvalue problems in modal analysis. Three predominant subspace algorithms, i.e., Krylov-Schur method, implicitly restarted Arnoldi method and Jacobi-Davidson method, are modified with some complementary techniques to make them suitable for modal analysis. De- tailed descriptions of the three algorithms are given. Based on these algorithms, a parallel solution procedure is established via the PANDA framework and its associated eigensolvers. Using the solution procedure on a machine equipped with up to 4800 processors, the parallel performance of the three predominant methods is evaluated via numerical experiments with typical en- gineering structures, where the maximum testing scale attains twenty million degrees of freedom. The speedup curves for dif- ferent cases are obtained and compared. The results show that the three methods are good for modal analysis in the scale of ten million degrees of freedom with a favorable parallel scalability.