%0 Journal Article %1 arbenz2005comparison %A Arbenz, Peter %A Hetmaniuk, Ulrich L. %A Lehoucq, Richard B. %A Tuminaro, Raymond S. %D 2005 %E 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. %J International Journal for Numerical Methods in Engineering %K 15a18-eigenvalues-singular-values-and-eigenvectors 15a22-matrix-pencils 65f08-preconditioners-for-iterative-methods 74h45-vibrations 74s05-finite-element-methods-for-solid-mechanics %N 2 %P 204–236 %R 10.1002/nme.1365 %T A comparison of eigensolvers for large‐scale 3D modal analysis using AMG‐preconditioned iterative methods %U https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.1365 %V 64 %X 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.

@article{arbenz2005comparison, 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.}, added-at = {2020-01-31T05:52:43.000+0100}, author = {Arbenz, Peter and Hetmaniuk, Ulrich L. and Lehoucq, Richard B. and Tuminaro, Raymond S.}, biburl = {https://www.bibsonomy.org/bibtex/2d620f7c983c7cf2287004b0afd42bb61/gdmcbain}, doi = {10.1002/nme.1365}, editor = {{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.}, interhash = {dd8ca8dc4e4529275ef7b7383c60d6b4}, intrahash = {d620f7c983c7cf2287004b0afd42bb61}, journal = {International Journal for Numerical Methods in Engineering}, keywords = {15a18-eigenvalues-singular-values-and-eigenvectors 15a22-matrix-pencils 65f08-preconditioners-for-iterative-methods 74h45-vibrations 74s05-finite-element-methods-for-solid-mechanics}, month = jun, number = 2, pages = {204–236}, timestamp = {2022-02-22T01:00:17.000+0100}, title = {A comparison of eigensolvers for large‐scale 3D modal analysis using AMG‐preconditioned iterative methods}, url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.1365}, volume = 64, year = 2005 }