A comparison of algorithms for modal analysis in the absence of a sparse direct method

The goal of our report is to compare a number of algorithms for computing a large number of eigenvectors of the generalized eigenvalue problem arising from a modal analysis of elastic structures using preconditioned iterative methods. The shift-invert Lanczos algorithm has emerged as the workhorse for the solution of this generalized eigenvalue problem; however a sparse direct method is required for the resulting set of linear equations. Instead, our report considers the use of preconditioned iterative method; in particular, we employ a scalable algebraic multigrid (AMG) preconditioner. We present a review of available preconditioned eigensolvers and a numerical comparison on two problems. Copyright c © 2003 John Wiley & Sons, Ltd.