A reduced order model for the finite element approximation of eigenvalue problems

Fleurianne Bertrand; Daniele Boffi; Abdul Halim

doi:10.1016/j.cma.2022.115696

A reduced order model for the finite element approximation of eigenvalue problems

Fleurianne Bertrand, Daniele Boffi, Abdul Halim

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

In this paper we consider a reduced order method for the approximation of the eigensolutions of the Laplace problem with Dirichlet boundary condition. We use a time continuation technique that consists in the introduction of a fictitious time parameter. We use a POD approach and we present some theoretical results showing how to choose the optimal dimension of the POD basis. The results of our computations confirm the optimal behavior of our approximate solution. We compute the first eigenvalue and discuss how to approximate the next eigenmodes.

Original language	English (US)
Pages (from-to)	115696
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	404
DOIs	https://doi.org/10.1016/j.cma.2022.115696
State	Published - Nov 28 2022

ASJC Scopus subject areas

General Physics and Astronomy
Mechanics of Materials
Mechanical Engineering
Computational Mechanics
Computer Science Applications

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10.1016/j.cma.2022.115696

https://repository.kaust.edu.sa/bitstream/10754/676874/5/1-s2.0-S004578252200651X-main.pdf

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title = "A reduced order model for the finite element approximation of eigenvalue problems",

abstract = "In this paper we consider a reduced order method for the approximation of the eigensolutions of the Laplace problem with Dirichlet boundary condition. We use a time continuation technique that consists in the introduction of a fictitious time parameter. We use a POD approach and we present some theoretical results showing how to choose the optimal dimension of the POD basis. The results of our computations confirm the optimal behavior of our approximate solution. We compute the first eigenvalue and discuss how to approximate the next eigenmodes.",

author = "Fleurianne Bertrand and Daniele Boffi and Abdul Halim",

note = "KAUST Repository Item: Exported on 2022-12-09 Acknowledged KAUST grant number(s): CRG2020 Acknowledgements: This research was supported by the Competitive Research Grants Program CRG2020 “Synthetic data-driven model reduction methods for modal analysis” awarded by the King Abdullah University of Science and Technology (KAUST). Daniele Boffi is member of the INdAM Research group GNCS and his research is partially supported by IMATI/CNR and by PRIN/MIUR.",

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T1 - A reduced order model for the finite element approximation of eigenvalue problems

AU - Bertrand, Fleurianne

AU - Boffi, Daniele

AU - Halim, Abdul

N1 - KAUST Repository Item: Exported on 2022-12-09 Acknowledged KAUST grant number(s): CRG2020 Acknowledgements: This research was supported by the Competitive Research Grants Program CRG2020 “Synthetic data-driven model reduction methods for modal analysis” awarded by the King Abdullah University of Science and Technology (KAUST). Daniele Boffi is member of the INdAM Research group GNCS and his research is partially supported by IMATI/CNR and by PRIN/MIUR.

PY - 2022/11/28

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N2 - In this paper we consider a reduced order method for the approximation of the eigensolutions of the Laplace problem with Dirichlet boundary condition. We use a time continuation technique that consists in the introduction of a fictitious time parameter. We use a POD approach and we present some theoretical results showing how to choose the optimal dimension of the POD basis. The results of our computations confirm the optimal behavior of our approximate solution. We compute the first eigenvalue and discuss how to approximate the next eigenmodes.

AB - In this paper we consider a reduced order method for the approximation of the eigensolutions of the Laplace problem with Dirichlet boundary condition. We use a time continuation technique that consists in the introduction of a fictitious time parameter. We use a POD approach and we present some theoretical results showing how to choose the optimal dimension of the POD basis. The results of our computations confirm the optimal behavior of our approximate solution. We compute the first eigenvalue and discuss how to approximate the next eigenmodes.

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A reduced order model for the finite element approximation of eigenvalue problems

Abstract

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