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Effective transmission conditions for thin-layer transmission problems in elastodynamics. The case of a planar layer model

hal.structure.identifierPropagation des Ondes : Étude Mathématique et Simulation [POEMS]
dc.contributor.authorBONNET, Marc
hal.structure.identifierPropagation des Ondes : Étude Mathématique et Simulation [POEMS]
hal.structure.identifierUniversité Paris-Sud - Paris 11 - Faculté des Sciences [UP11 UFR Sciences]
dc.contributor.authorBUREL, Aliénor
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierAdvanced 3D Numerical Modeling in Geophysics [Magique 3D]
dc.contributor.authorDURUFLÉ, Marc
hal.structure.identifierPropagation des Ondes : Étude Mathématique et Simulation [POEMS]
dc.contributor.authorJOLY, Patrick
dc.date.accessioned2024-04-04T03:18:34Z
dc.date.available2024-04-04T03:18:34Z
dc.date.issued2016
dc.identifier.issn0764-583X
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/194421
dc.description.abstractEnThis article is concerned with the design, analysis, numerical approximation and implementation of effective transmission conditions (ETCs) for the propagation of elastic waves through a thin planar elastic layer with small uniform thickness η which is embedded in a reference elastic medium, under transient conditions, with both materials assumed to have isotropic properties. A family of ETCs of order k (i.e. whose approximation error is of expected order O(η k+1)) is formulated by deriving and exploiting a formal asymptotic expansion in powers of η of the transmission solution inside the layer. The second-order ETCs are then retained as the main focus for the remainder of the article, and given a full justification in terms of both the stability of the resulting transient elastodynamic problem and the error analysis. The latter is performed by establishing and justifying asymptotic expansions for the solutions of both the exact transmission problem and its approximation based on the second-order ETCs. As a result, the error (in energy norm) between those two solutions is shown to be, as expected, of order O(η 3). Finally, the numerical approximation of the proposed second-order ETC within the framework of spectral element methods is studied, with special attention devoted to the selection of a robust time-stepping scheme that is mostly explicit (and conditionally stable). Among these, a scheme that is implicit only for the interfacial degrees of freedom, termed semi-implicit, is shown to be stable under the same stability condition as for the layer-less configuration. The main theoretical results of this work are illustrated and validated by 2D and 3D numerical experiments under transient elastodynamic conditions.
dc.language.isoen
dc.publisherEDP Sciences
dc.subject.en65N30
dc.subject.en35C20
dc.subject.en2015
dc.subject.en74B05
dc.subject.en65N12
dc.title.enEffective transmission conditions for thin-layer transmission problems in elastodynamics. The case of a planar layer model
dc.typeArticle de revue
dc.identifier.doi10.1051/m2an/2015030
dc.subject.halInformatique [cs]/Modélisation et simulation
bordeaux.journalESAIM: Mathematical Modelling and Numerical Analysis
bordeaux.page43-75
bordeaux.volume50
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01144401
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01144401v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=ESAIM:%20Mathematical%20Modelling%20and%20Numerical%20Analysis&rft.date=2016&rft.volume=50&rft.spage=43-75&rft.epage=43-75&rft.eissn=0764-583X&rft.issn=0764-583X&rft.au=BONNET,%20Marc&BUREL,%20Ali%C3%A9nor&DURUFL%C3%89,%20Marc&JOLY,%20Patrick&rft.genre=article


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