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Algebraic multigrid methods for solving generalized eigenvalue problems
Author(s) -
Borzì Alfio,
Borzì Giuseppe
Publication year - 2006
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1478
Subject(s) - multigrid method , preconditioner , conjugate gradient method , mathematics , eigenvalues and eigenvectors , isospectral , linear system , block (permutation group theory) , algebraic number , inverse iteration , mathematical optimization , iterative method , mathematical analysis , partial differential equation , geometry , physics , quantum mechanics
Three algebraic multigrid (AMG) methods for solving generalized eigenvalue problems are presented. The first method combines modern AMG techniques with a non‐linear multigrid approach and nested iteration strategy. The second method is a preconditioned inverse iteration with linear AMG preconditioner. The third method is an enhancement of the previous one, namely the locally optimal block preconditioned conjugate gradient. Efficiency and accuracy of solutions computed by these AMG eigensolvers are validated on standard benchmarks where part of the spectrum is known. In particular, the problem of isospectral drums is addressed. Copyright © 2005 John Wiley & Sons, Ltd.