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Generalized finite element methods for quadratic eigenvalue problems

Axel Målqvist (Institutionen för matematiska vetenskaper, Tillämpad matematik och statistik) ; Daniel Peterseim
ESAIM: Modelisation Mathematique et Analyse Numerique (0764-583X). Vol. 51 (2017), 1, p. 147 - 163.
[Artikel, refereegranskad vetenskaplig]

We consider a large-scale quadratic eigenvalue problem (QEP), formulated using P1 finite elements on a fine scale reference mesh. This model describes damped vibrations in a structural mechanical system. In particular we focus on problems with rapid material data variation, e.g., composite materials. We construct a low dimensional generalized finite element (GFE) space based on the localized orthogonal decomposition (LOD) technique. The construction involves the (parallel) solution of independent localized linear Poisson-type problems. The GFE space is used to compress the large-scale algebraic QEP to a much smaller one with a similar modeling accuracy. The small scale QEP can then be solved by standard techniques at a significantly reduced computational cost. We prove convergence with rate for the proposed method and numerical experiments confirm our theoretical findings.

Nyckelord: Quadratic eigenvalue problem ; finite element ; localized orthogonal decomposition



Denna post skapades 2016-12-22. Senast ändrad 2017-04-28.
CPL Pubid: 246489

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, Tillämpad matematik och statistikInstitutionen för matematiska vetenskaper, Tillämpad matematik och statistik (GU)

Ämnesområden

Matematik

Chalmers infrastruktur