Generalized finite element methods for quadratic eigenvalue problems
Artikel i vetenskaplig tidskrift, 2017

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.

Quadratic eigenvalue problem

localized orthogonal decomposition

finite element

Författare

Axel Målqvist

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Daniel Peterseim

Mathematical Modelling and Numerical Analysis

0764-583X (ISSN) 1290-3841 (eISSN)

Vol. 51 1 147 - 163

Ämneskategorier

Matematik

Fundament

Grundläggande vetenskaper

DOI

10.1051/m2an/2016019

Mer information

Skapat

2017-10-08