Fritzen, Felix ; Haasdonk, Bernard ; Ryckelynck, David ; Schöps, Sebastian (2023)
An Algorithmic Comparison of the Hyper-Reduction and the Discrete Empirical Interpolation Method for a Nonlinear Thermal Problem.
In: Mathematical and Computational Applications, 2018, 23 (1)
doi: 10.26083/tuprints-00016945
Artikel, Zweitveröffentlichung, Verlagsversion
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Kurzbeschreibung (Abstract)
A novel algorithmic discussion of the methodological and numerical differences of competing parametric model reduction techniques for nonlinear problems is presented. First, the Galerkin reduced basis (RB) formulation is presented, which fails at providing significant gains with respect to the computational efficiency for nonlinear problems. Renowned methods for the reduction of the computing time of nonlinear reduced order models are the Hyper-Reduction and the (Discrete) Empirical Interpolation Method (EIM, DEIM). An algorithmic description and a methodological comparison of both methods are provided. The accuracy of the predictions of the hyper-reduced model and the (D)EIM in comparison to the Galerkin RB is investigated. All three approaches are applied to a simple uncertainty quantification of a planar nonlinear thermal conduction problem. The results are compared to computationally intense finite element simulations.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2023 |
| Autor(en): | Fritzen, Felix ; Haasdonk, Bernard ; Ryckelynck, David ; Schöps, Sebastian |
| Art des Eintrags: | Zweitveröffentlichung |
| Titel: | An Algorithmic Comparison of the Hyper-Reduction and the Discrete Empirical Interpolation Method for a Nonlinear Thermal Problem |
| Sprache: | Englisch |
| Publikationsjahr: | 20 November 2023 |
| Ort: | Darmstadt |
| Publikationsdatum der Erstveröffentlichung: | 2018 |
| Ort der Erstveröffentlichung: | Basel |
| Verlag: | MDPI |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Mathematical and Computational Applications |
| Jahrgang/Volume einer Zeitschrift: | 23 |
| (Heft-)Nummer: | 1 |
| Kollation: | 25 Seiten |
| DOI: | 10.26083/tuprints-00016945 |
| URL / URN: | https://tuprints.ulb.tu-darmstadt.de/16945 |
| Zugehörige Links: | |
| Herkunft: | Zweitveröffentlichung DeepGreen |
| Kurzbeschreibung (Abstract): | A novel algorithmic discussion of the methodological and numerical differences of competing parametric model reduction techniques for nonlinear problems is presented. First, the Galerkin reduced basis (RB) formulation is presented, which fails at providing significant gains with respect to the computational efficiency for nonlinear problems. Renowned methods for the reduction of the computing time of nonlinear reduced order models are the Hyper-Reduction and the (Discrete) Empirical Interpolation Method (EIM, DEIM). An algorithmic description and a methodological comparison of both methods are provided. The accuracy of the predictions of the hyper-reduced model and the (D)EIM in comparison to the Galerkin RB is investigated. All three approaches are applied to a simple uncertainty quantification of a planar nonlinear thermal conduction problem. The results are compared to computationally intense finite element simulations. |
| Freie Schlagworte: | model order reduction (MOR), reduced basis model order reduction (RB MOR), uncertainty quantification (UQ), (discrete) empirical interpolation method (EIM, DEIM), hyper-reduction (HR) |
| Status: | Verlagsversion |
| URN: | urn:nbn:de:tuda-tuprints-169455 |
| Zusätzliche Informationen: | This article belongs to the Section Engineering |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 000 Allgemeines, Informatik, Informationswissenschaft > 004 Informatik 600 Technik, Medizin, angewandte Wissenschaften > 621.3 Elektrotechnik, Elektronik |
| Fachbereich(e)/-gebiet(e): | 18 Fachbereich Elektrotechnik und Informationstechnik 18 Fachbereich Elektrotechnik und Informationstechnik > Institut für Teilchenbeschleunigung und Theorie Elektromagnetische Felder Exzellenzinitiative Exzellenzinitiative > Graduiertenschulen Exzellenzinitiative > Graduiertenschulen > Graduate School of Computational Engineering (CE) |
| Hinterlegungsdatum: | 20 Nov 2023 15:10 |
| Letzte Änderung: | 27 Nov 2023 11:15 |
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| Suche nach Titel in: | TUfind oder in Google |
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- An Algorithmic Comparison of the Hyper-Reduction and the Discrete Empirical Interpolation Method for a Nonlinear Thermal Problem. (deposited 20 Nov 2023 15:10) [Gegenwärtig angezeigt]
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