A discretize-then-map approach for the treatment of parameterized geometries in model order reduction
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Modeling Enablers for Multi-PHysics and InteractionS [MEMPHIS] | |
| dc.contributor.author | TADDEI, Tommaso | |
| hal.structure.identifier | Modeling Enablers for Multi-PHysics and InteractionS [MEMPHIS] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | ZHANG, Lei | |
| dc.date.accessioned | 2024-04-04T02:33:56Z | |
| dc.date.available | 2024-04-04T02:33:56Z | |
| dc.date.issued | 2021-10-01 | |
| dc.identifier.issn | 0045-7825 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190519 | |
| dc.description.abstractEn | We propose a new general approach for the treatment of parameterized geometries in projection-based model order reduction. During the offline stage, given (i) a family of parameterized domains $\{ \Omega_{\mu}: \mu \in \mathcal{P} \} \subset \mathbb{R}^D$ where $\mu \in \mathcal{P} \subset \mathbb{R}^P$ denotes a vector of parameters, (ii) a parameterized mapping $\underline{\Phi}_{\mu}$ between a reference domain $\Omega$ and the parameter-dependent domain $\Omega_{\mu}$, and (iii) a finite element triangulation of $\Omega$, we resort to an empirical quadrature procedure to select a subset of the elements of the grid. During the online stage, we first use the mapping to "move" the nodes of the selected elements and then we use standard element-wise residual evaluation routines to evaluate the residual and possibly its Jacobian. We discuss how to devise an online-efficient reduced-order model and we discuss the differences with the more standard "map-then-discretize" approach (e.g., Rozza, Huynh, Patera, ACME, 2007); in particular, we show how the discretize-then-map framework greatly simplifies the implementation of the reduced-order model. We apply our approach to a two-dimensional potential flow problem past a parameterized airfoil, and to the two-dimensional RANS simulations of the flow past the Ahmed body. | |
| dc.language.iso | en | |
| dc.publisher | Elsevier | |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc/ | |
| dc.subject.en | Parameterized partial differential equations | |
| dc.subject.en | Model order reduction | |
| dc.subject.en | Parameterized geometries | |
| dc.title.en | A discretize-then-map approach for the treatment of parameterized geometries in model order reduction | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1016/j.cma.2021.113956 | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.subject.hal | Mathématiques [math]/Physique mathématique [math-ph] | |
| dc.identifier.arxiv | 2010.13935 | |
| dc.description.sponsorshipEurope | Accurate Roms for Industrial Applications | |
| bordeaux.journal | Computer Methods in Applied Mechanics and Engineering | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-03120853 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-03120853v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Computer%20Methods%20in%20Applied%20Mechanics%20and%20Engineering&rft.date=2021-10-01&rft.eissn=0045-7825&rft.issn=0045-7825&rft.au=TADDEI,%20Tommaso&ZHANG,%20Lei&rft.genre=article |
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