Performance Evaluation of a Multilevel Sub-structuring Method for Sparse Eigenvalue Problems

Abstract

The automated multilevel sub-structuring (AMLS) method [2, 7, 3] is an extension of a simple sub-structuring method called component mode synthesis (CMS) [6, 4] originally developed in the 1960s. The recent work by Bennighof and Lehoucq [3] provides a high level mathematical description of the AMLS method in a continuous variational setting, as well as a framework for describing AMLS in matrix algebra notations. The AMLS approach has been successfully used in vibration and acoustic analysis of very large scale finite element models of automobile bodies [7]. In this paper, we evaluate the performance of AMLS on other types of applications. Similar to the domain decomposition techniques used in solving linear systems, AMLS reduces a large-scale eigenvalue problem to a sequence of smaller problems that are easier to solve. The method is amenable to an efficient parallel implementation. However, a few questions regarding the accuracy and computational efficiency of the method remain to be carefully examined. Our earlier paper [12] addressed some of these questions for a single-level algorithm. We developed a simple criterion for choosing spectral components from each sub-structure, performed algebraic analysis based on this mode selection criterion, and derived error bounds for the approximate eigenpair associated with the smallest eigenvalue. This paper focuses on the performance of the multilevel algorithm.