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dc.contributor.authorCocquet, Pierre-Henri
dc.contributor.authorRiffo, Sebastián
dc.contributor.authorSalomon, Julien
dc.date.accessioned2020-04-03T09:59:41Z
dc.date.available2020-04-03T09:59:41Z
dc.date.issued2020
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/20606
dc.language.isoenen
dc.subjectBathymetryen
dc.subjectlong wavesen
dc.subject.ddc515en
dc.titleOptimization of Bathymetry for Long Waves with Small Amplitudeen
dc.typeDocument de travail / Working paper
dc.description.abstractenThis paper deals with bathymetry-oriented optimization in the case of long waves with small amplitude. Under these two assumptions, the free-surface incompressible Navier-Stokes system can be written as a wave equation where the bathymetry appears as a parameter in the spatial operator. Looking then for time-harmonic fields and writing the bottom topography as a perturbation of a flat bottom, we end up with a heterogeneous Helmholtz equation with impedance boundary condition. In this way, we study some PDE-constrained optimization problem for a Helmholtz equation in heterogeneous media whose coefficients are only bounded with bounded variation. We provide necessary condition for a general cost function to have at least one optimal solution. We also prove the convergence of a finite element approximation of the solution to the considered Helmholtz equation as well as the convergence of discrete optimum toward the continuous ones. We end this paper with some numerical experiments to illustrate the theoretical results and show that some of their assumptions could actually be removed.en
dc.publisher.nameCahier de recherche CEREMADE, Université Paris-Dauphineen
dc.publisher.cityParisen
dc.identifier.citationpages27en
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-02511976en
dc.subject.ddclabelAnalyseen
dc.identifier.citationdate2020-03
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2020-04-03T09:54:55Z
hal.person.labIds209018
hal.person.labIds60
hal.person.labIds25


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