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Registration-based model reduction in complex two-dimensional geometries

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierModeling Enablers for Multi-PHysics and InteractionS [MEMPHIS]
dc.contributor.authorTADDEI, Tommaso
hal.structure.identifierModeling Enablers for Multi-PHysics and InteractionS [MEMPHIS]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorZHANG, Lei
dc.date.accessioned2024-04-04T02:47:34Z
dc.date.available2024-04-04T02:47:34Z
dc.date.issued2021-08-04
dc.identifier.issn0885-7474
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191654
dc.description.abstractEnWe present a general -- i.e., independent of the underlying equation -- registration procedure for parameterized model order reduction. Given the spatial domain $\Omega \subset \mathbb{R}^2$ and the manifold $\mathcal{M}= \{ u_{\mu} : \mu \in \mathcal{P} \}$ associated with the parameter domain $\mathcal{P} \subset \mathbb{R}^P$ and the parametric field $\mu \mapsto u_{\mu} \in L^2(\Omega)$, our approach takes as input a set of snapshots $\{ u^k \}_{k=1}^{n_{\rm train}} \subset \mathcal{M}$ and returns a parameter-dependent bijective mapping $\underline{\Phi}: \Omega \times \mathcal{P} \to \mathbb{R}^2$: the mapping is designed to make the mapped manifold $\{ u_{\mu} \circ \underline{\Phi}_{\mu}: \, \mu \in \mathcal{P} \}$ more amenable for linear compression methods. In this work, we extend and further analyze the registration approach proposed in [Taddei, SISC, 2020]. The contributions of the present work are twofold. First, we extend the approach to deal with annular domains by introducing a suitable transformation of the coordinate system. Second, we discuss the extension to general two-dimensional geometries: towards this end, we introduce a spectral element approximation, which relies on a partition $\{ \Omega_{q} \}_{q=1} ^{N_{\rm dd}}$ of the domain $\Omega$ such that $\Omega_1,\ldots,\Omega_{N_{\rm dd}}$ are isomorphic to the unit square. We further show that our spectral element approximation can cope with parameterized geometries. We present rigorous mathematical analysis to justify our proposal; furthermore, we present numerical results for a heat-transfer problem in an annular domain and for a potential flow past a rotating airfoil to demonstrate the effectiveness of our method.
dc.language.isoen
dc.publisherSpringer Verlag
dc.subject.enParameterized partial differential equations
dc.subject.enModel order reduction
dc.subject.enRegistration methods
dc.subject.enNonlinear approximations
dc.title.enRegistration-based model reduction in complex two-dimensional geometries
dc.typeArticle de revue
dc.identifier.doi10.1007/s10915-021-01584-y
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.subject.halMathématiques [math]/Analyse numérique [math.NA]
dc.identifier.arxiv2101.10259
dc.description.sponsorshipEuropeAccurate Roms for Industrial Applications
bordeaux.journalJournal of Scientific Computing
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-03121165
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-03121165v1
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