A one-shot overlapping Schwarz method for component-based model reduction: application to nonlinear elasticity
| hal.structure.identifier | Modeling Enablers for Multi-PHysics and InteractionS [MEMPHIS] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | IOLLO, Angelo | |
| hal.structure.identifier | Modeling Enablers for Multi-PHysics and InteractionS [MEMPHIS] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | SAMBATARO, Giulia | |
| hal.structure.identifier | Modeling Enablers for Multi-PHysics and InteractionS [MEMPHIS] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | TADDEI, Tommaso | |
| dc.date.accessioned | 2024-04-04T02:36:58Z | |
| dc.date.available | 2024-04-04T02:36:58Z | |
| dc.date.issued | 2023-02 | |
| dc.identifier.issn | 0045-7825 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190766 | |
| dc.description.abstractEn | We propose a component-based (CB) parametric model order reduction (pMOR) formulation for parameterized nonlinear elliptic partial differential equations (PDEs) based on overlapping subdomains. Our approach reads as a constrained optimization statement that penalizes the jump at the components’ interfaces subject to the approximate satisfaction of the PDE in each local subdomain. Furthermore, the approach relies on the decomposition of the local states into a port component – associated with the solution on interior boundaries – and a bubble component that vanishes at ports: since the bubble components are uniquely determined by the solution value at the corresponding port, we can recast the constrained optimization statement into an unconstrained statement, which reads as a nonlinear least-squares problem and can be solved using the Gauss–Newton method. We present thorough numerical investigations for a two-dimensional neo-Hookean nonlinear mechanics problem to validate our method; we further discuss the well-posedness of the mathematical formulation and the a priori error analysis for linear coercive problems. | |
| dc.language.iso | en | |
| dc.publisher | Elsevier | |
| dc.subject.en | parameterized partial differential equations | |
| dc.subject.en | model order reduction | |
| dc.subject.en | overlapping domain decom- position | |
| dc.subject.en | alternating Schwarz method | |
| dc.title.en | A one-shot overlapping Schwarz method for component-based model reduction: application to nonlinear elasticity | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1016/j.cma.2022.115786 | |
| dc.subject.hal | Mathématiques [math]/Analyse numérique [math.NA] | |
| dc.identifier.arxiv | 2207.05426 | |
| dc.description.sponsorshipEurope | Accurate Roms for Industrial Applications | |
| bordeaux.journal | Computer Methods in Applied Mechanics and Engineering | |
| bordeaux.page | 115786 | |
| bordeaux.volume | 404 | |
| 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-03910506 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-03910506v1 | |
| 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=2023-02&rft.volume=404&rft.spage=115786&rft.epage=115786&rft.eissn=0045-7825&rft.issn=0045-7825&rft.au=IOLLO,%20Angelo&SAMBATARO,%20Giulia&TADDEI,%20Tommaso&rft.genre=article |
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