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Stability analysis of the POD reduced order method for solving the bidomain model in cardiac electrophysiology

hal.structure.identifierModélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]
dc.contributor.authorCORRADO, Cesare
hal.structure.identifierLaboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis] [LR-LAMSIN-ENIT]
dc.contributor.authorLASSOUED, Jamila
hal.structure.identifierTunis El Manar University [University of Tunis El Manar] [Tunisia] = Université de Tunis El Manar [Tunisie] = جامعة تونس المنار (ar) [UTM]
hal.structure.identifierLaboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis] [LR-LAMSIN-ENIT]
dc.contributor.authorMAHJOUB, Moncef
hal.structure.identifierModélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]
dc.contributor.authorZEMZEMI, Nejib
dc.date.accessioned2024-04-04T03:16:43Z
dc.date.available2024-04-04T03:16:43Z
dc.date.issued2015-12-04
dc.identifier.issn0025-5564
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/194241
dc.description.abstractEnIn this work we show the numerical stability of the Proper Orthogonal Decomposition (POD) reduced order method used in cardiac electrophysiology applications. The difficulty of proving the stability comes from the fact that we are interested in the bidomain model, which is a system of degenerate parabolic equations coupled to a system of ODEs representing the cell membrane electrical activity. The proof of the stability of this method is based an a priori estimate controlling the gap between the reduced order solution and the Galerkin finite element one. We present some numerical simulations confirming the theoretical results. We also combine the POD method with a time splitting scheme allowing a faster solution of the bidomain problem and show numerical results. Finally, we conduct numerical simulation in 2D illustrating the stability of the POD method in its sensitivity to the ionic model parameters. We also perform 3D simulation using a massively parallel code. We show the computational gain using the POD reduced order model. We also show that this method has a better scalability than the full finite element method.
dc.description.sponsorshipL'Institut de Rythmologie et modélisation Cardiaque - ANR-10-IAHU-0004
dc.language.isoen
dc.publisherElsevier
dc.subject.enproper orthogonal decomposition
dc.subject.enreduced order method
dc.subject.enBidomain equation
dc.subject.ena priori estimates
dc.subject.enionic parameters
dc.subject.enstability analysis
dc.subject.enMitchell-Schaeffer model
dc.title.enStability analysis of the POD reduced order method for solving the bidomain model in cardiac electrophysiology
dc.typeArticle de revue
dc.identifier.doi10.1016/j.mbs.2015.12.005
dc.subject.halInformatique [cs]/Modélisation et simulation
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
bordeaux.journalMathematical Biosciences
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01245685
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01245685v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Mathematical%20Biosciences&rft.date=2015-12-04&rft.eissn=0025-5564&rft.issn=0025-5564&rft.au=CORRADO,%20Cesare&LASSOUED,%20Jamila&MAHJOUB,%20Moncef&ZEMZEMI,%20Nejib&rft.genre=article


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