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| HAL : hal-00590812, version 1 |
| DOI : 10.1051/proc/201134006 |
| Fiche détaillée |  Récupérer au format |
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| Summer school on multiresolution and adaptive mesh refinement methods, E. Cancès, V. Louvet, M. Massot (Ed.) (2011) Vol. 34 277-290 |
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| New Resolution Strategy for Multi-scale Reaction Waves using Time Operator Splitting and Space Adaptive Multiresolution: Application to Human Ischemic Stroke |
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Max Duarte 1Marc Massot 1 |
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| PEPS Maths-ST2I project MIPAC Collaboration(s) |
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| (22/12/2011) |
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| We tackle the numerical simulation of reaction-diffusion equations modeling multi-scale reaction waves. This type of problems induces peculiar difficulties and potentially large stiffness which stem from the broad spectrum of temporal scales in the nonlinear chemical source term as well as from the presence of large spatial gradients in the reactive fronts, spatially very localized. In this paper, we introduce a new resolution strategy based on time operator splitting and space adaptive multiresolution in the context of very localized and stiff reaction fronts. Based on recent theoretical studies of numerical analysis, such a strategy leads to a splitting time step which is not restricted neither by the fastest scales in the source term nor by restrictive diffusive step stability limits, but only by the physics of the phenomenon. We aim thus at solving accurately complete models including all time and space scales of the phenomenon, considering large simulation domains with conventional computing resources. The efficiency of the method is evaluated through 2D and 3D numerical simulations of a human ischemic stroke model, conducted on a simplified brain geometry, for which a simple parallelization strategy for shared memory architectures was implemented, in order to reduce computing costs related to "detailed chemistry" features of the model. |
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| 1 : | Laboratoire d'Énergétique Moléculaire et Macroscopique, Combustion (EM2C) |
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CNRS : UPR288 – Ecole Centrale Paris |
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| 2 : | Laboratoire Jean Alexandre Dieudonné (JAD) |
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CNRS : UMR6621 – Université Nice Sophia Antipolis [UNS] |
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| 3 : | Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur [Orsay] (LIMSI) |
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CNRS : UPR3251 – Université Pierre et Marie Curie [UPMC] - Paris VI – Université Paris XI - Paris Sud |
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| 4 : | Institut Camille Jordan (ICJ) |
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CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon |
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| 5 : | NUMED (ENS Lyon / UCB Lyon / Inria Grenoble Rhône-Alpes) |
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Université Claude Bernard - Lyon I – INRIA – École Normale Supérieure - Lyon – CNRS : UMR5669 – Unité de Mathématiques Pures et Appliquées |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles Informatique/Modélisation et simulation Informatique/Calcul parallèle, distribué et partagé |
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| Reaction-diffusion – Operator splitting – Adaptive multiresolution – Ischemic stroke – Parallel computing |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00590812, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00590812 | |
| oai:hal.archives-ouvertes.fr:hal-00590812 | |
| Contributeur : Max Duarte | |
| Soumis le : Samedi 7 Mai 2011, 13:36:52 | |
| Dernière modification le : Vendredi 18 Janvier 2013, 14:41:19 | |
