Generalized finite element methods for quadratic eigenvalue problems
Generalized finite element methods for quadratic eigenvalue problems
dc.contributor.author | Målqvist, Axel | |
dc.contributor.author | Peterseim, Daniel | |
dc.date.accessioned | 2024-08-21T09:55:06Z | |
dc.date.available | 2024-08-21T09:55:06Z | |
dc.date.issued | 10.2015 | |
dc.identifier.uri | https://hdl.handle.net/20.500.11811/11901 | |
dc.description.abstract | 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 then 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. | en |
dc.format.extent | 24 | |
dc.language.iso | eng | |
dc.relation.ispartofseries | INS Preprints ; 1522 | |
dc.rights | In Copyright | |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | |
dc.subject | Quadratic eigenvalue problem | |
dc.subject | finite element | |
dc.subject | localized orthogonal decomposition | |
dc.subject.ddc | 510 Mathematik | |
dc.subject.ddc | 518 Numerische Analysis | |
dc.title | Generalized finite element methods for quadratic eigenvalue problems | |
dc.type | Preprint | |
dc.publisher.name | Institut für Numerische Simulation (INS) | |
dc.publisher.location | Bonn | |
dc.rights.accessRights | openAccess | |
dc.relation.doi | https://doi.org/10.1051/m2an/2016019 | |
ulbbn.pubtype | Zweitveröffentlichung | |
dcterms.bibliographicCitation.url | https://ins.uni-bonn.de/publication/preprints |
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