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vibro ‐Lanczos, a symmetric Lanczos solver for vibro‐acoustic simulations
Author(s) -
Tabak Umut,
Rixen Daniel J.
Publication year - 2016
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.5170
Subject(s) - lanczos resampling , orthogonalization , eigenvalues and eigenvectors , solver , discretization , mathematics , lanczos algorithm , finite element method , transformation (genetics) , matrix (chemical analysis) , symmetric matrix , generalized minimal residual method , mathematical optimization , mathematical analysis , iterative method , algorithm , physics , biochemistry , chemistry , materials science , quantum mechanics , gene , composite material , thermodynamics
Summary An efficient symmetric Lanczos method for the solution of vibro‐acoustic eigenvalue problems is presented in this paper. Although finite element discretization results in real but nonsymmetric system matrices, we show that an efficient iteration scheme on a symmetric representation can be built up by using a transformation matrix. In order to decrease the numerical costs of the orthogonalizations performed, we propose to use a partial orthogonalization scheme for the symmetric case. The proposed method is tested on two large problems in order to demonstrate its efficiency and accuracy. Copyright © 2016 John Wiley & Sons, Ltd.