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Carleman-based reconstruction algorithm for the waves

hal.structure.identifierÉquipe Méthodes et Algorithmes en Commande [LAAS-MAC]
dc.contributor.authorBAUDOUIN, Lucie
hal.structure.identifierMathématiques Appliquées Paris 5 [MAP5 - UMR 8145]
hal.structure.identifierCentre National de la Recherche Scientifique [CNRS]
dc.contributor.authorDE BUHAN, Maya
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierCentre National de la Recherche Scientifique [CNRS]
dc.contributor.authorERVEDOZA, Sylvain
hal.structure.identifierCenter for Mathematical Modeling [CMM]
hal.structure.identifierDepartamento de Ingeniería Matemática [Santiago] [DIM]
dc.contributor.authorOSSES, Axel
dc.date.accessioned2024-04-04T02:57:31Z
dc.date.available2024-04-04T02:57:31Z
dc.date.issued2021-04
dc.identifier.issn0036-1429
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192572
dc.description.abstractEnWe present a globally convergent numerical algorithm based on global Carleman estimates to reconstruct the speed of propagation of waves in a bounded domain with Dirichlet boundary conditions from a single measurement of the boundary flux of the solutions in a finite time interval. The global convergence of the proposed algorithm naturally arises from the proof of the Lipschitz stability of the corresponding inverse problem for both sufficiently large observation time and boundary using global Carleman inequalities. The speed of propagation is supposed to be independent of time but varying in space with a trace and normal derivative known at the boundary and belonging to a certain admissible set that limits the speed fluctuations with respect to a given exterior point x0. In order to recover the speed, we also require a single experiment with null initial velocity and initial deformation having some monotonicity properties in the direction of x − x0. We perform numerical simulations in the discrete setting in order to illustrate and to validate the feasibility of the algorithm in both one and two dimensions in space. As proved theoretically, we verify that the numerical reconstruction is achieved for any admissible initial guess, even in the presence of small random disturbances on the measurements.
dc.description.sponsorshipSynthèse d'observateur pour des systèmes de dimension infinie - ANR-19-CE48-0004
dc.language.isoen
dc.publisherSociety for Industrial and Applied Mathematics
dc.subject.enhyperbolic equation
dc.subject.eninverse problem
dc.subject.enreconstruction algorithm
dc.subject.enCarleman estimates AMS subject classifications
dc.title.enCarleman-based reconstruction algorithm for the waves
dc.typeArticle de revue
dc.identifier.doi10.1137/20M1315798
dc.subject.halMathématiques [math]
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.subject.halMathématiques [math]/Analyse numérique [math.NA]
dc.subject.halMathématiques [math]/Optimisation et contrôle [math.OC]
bordeaux.journalSIAM Journal on Numerical Analysis
bordeaux.page998–1039
bordeaux.volume59
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue2
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-02458787
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-02458787v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=SIAM%20Journal%20on%20Numerical%20Analysis&rft.date=2021-04&rft.volume=59&rft.issue=2&rft.spage=998%E2%80%931039&rft.epage=998%E2%80%931039&rft.eissn=0036-1429&rft.issn=0036-1429&rft.au=BAUDOUIN,%20Lucie&DE%20BUHAN,%20Maya&ERVEDOZA,%20Sylvain&OSSES,%20Axel&rft.genre=article


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