Abstract

The goal of our paper is to compare a number of algorithms for computing a large number of eigenvectors of the generalized symmetric eigenvalue problem arising from a modal analysis of elastic structures. The shift-invert Lanczos algorithm has emerged as the workhorse for the solution of this generalized eigenvalue problem; however, a sparse direct factorization is required for the resulting set of linear equations. Instead, our paper considers the use of preconditioned iterative methods. We present a brief review of available preconditioned eigensolvers followed by a numerical comparison on three problems using a scalable algebraic multigrid (AMG) preconditioner.

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