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

Abstract

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. Detailed 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 engineering structures, where the maximum testing scale attains twenty million degrees of freedom. The speedup curves for different 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.