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Localized model reduction for nonlinear elliptic partial differential equations: localized training, partition of unity, and adaptive enrichment

hal.structure.identifierDepartment of Electrical and Computer Engineering
dc.contributor.authorSMETANA, Kathrin
hal.structure.identifierModeling Enablers for Multi-PHysics and InteractionS [MEMPHIS]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorTADDEI, Tommaso
dc.date.accessioned2024-04-04T02:36:57Z
dc.date.available2024-04-04T02:36:57Z
dc.date.issued2023-06-15
dc.identifier.issn1064-8275
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/190765
dc.description.abstractEnWe propose a component-based (CB) parametric model order reduction (pMOR) formulation for parameterized nonlinear elliptic partial differential equations (PDEs). CB-pMOR is designed to deal with large-scale problems for which full-order solves are not affordable in a reasonable time frame or parameters' variations induce topology changes that prevent the application of monolithic pMOR techniques. We rely on the partition-of-unity method (PUM) to devise global approximation spaces from local reduced spaces, and on Galerkin projection to compute the global state estimate. We propose a randomized data compression algorithm based on oversampling for the construction of the components' reduced spaces: the approach exploits random boundary conditions of controlled smoothness on the oversampling boundary. We further propose an adaptive residual-based enrichment algorithm that exploits global reduced-order solves on representative systems to update the local reduced spaces. We prove exponential convergence of the enrichment procedure for linear coercive problems; we further present numerical results for a two-dimensional nonlinear diffusion problem to illustrate the many features of our proposal and demonstrate its effectiveness.
dc.language.isoen
dc.publisherSociety for Industrial and Applied Mathematics
dc.subject.enparameterized partial differential equations
dc.subject.enmodel order reduction
dc.subject.endomain decomposition
dc.title.enLocalized model reduction for nonlinear elliptic partial differential equations: localized training, partition of unity, and adaptive enrichment
dc.typeArticle de revue
dc.identifier.doi10.1137/22M148402X
dc.subject.halMathématiques [math]/Analyse numérique [math.NA]
bordeaux.journalSIAM Journal on Scientific Computing
bordeaux.pageA1300-A1331
bordeaux.volume45
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue3
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-03910541
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-03910541v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=SIAM%20Journal%20on%20Scientific%20Computing&rft.date=2023-06-15&rft.volume=45&rft.issue=3&rft.spage=A1300-A1331&rft.epage=A1300-A1331&rft.eissn=1064-8275&rft.issn=1064-8275&rft.au=SMETANA,%20Kathrin&TADDEI,%20Tommaso&rft.genre=article


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