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Eigenvalue extraction for large finite element models using a new conjugate gradient algorithm

✍ Scribed by Lafreniere, R. A. ;Accorsi, M. L.

Publisher: John Wiley and Sons
Year: 1996
Tongue: English
Weight: 311 KB
Volume: 12
Category: Article
ISSN: 1069-8299
DOI: 10.1002/(sici)1099-0887(199602)12:2<77::aid-cnm953>3.0.co;2-7

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✦ Synopsis

A new conjugate gradient algorithm is presented for extracting eigenvalues from large systems of equations encountered in finite element analysis. The new algorithm involves applying the conjugate gradient method (CGM) to a static problem to generate an equivalent tridiagonal matrix used for eigenvalue computation. The eigenvalues of the tridiagonal matrix are then extracted using a QR factorization. The similarity of the new CGM with the Lanczos method is discussed regarding the need for matrix inversion and reorthogonalization. Several examples using the new method are presented to illustrate its performance.

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