New Resolution Strategy for Multi-scale Reaction Waves using Time Operator Splitting and Space Adaptive Multiresolution: Application to Human Ischemic Stroke
ESAIM. Proceedings, Tome 34 (2011), pp. 277-290
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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. A new resolution strategy was recently introduced ? that combines a performing time operator splitting with high oder dedicated time integration methods and space adaptive multiresolution. 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 stability limits related to the diffusion problem, but only by the physics of the phenomenon. In this paper, 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.
Affiliations des auteurs :
Max Duarte 1, 2 ; Marc Massot 1 ; Stéphane Descombes 3 ; Christian Tenaud 4 ; Thierry Dumont 5 ; Violaine Louvet 5 ; Frédérique Laurent 1
@article{EP_2011_34_a6,
author = {Max Duarte and Marc Massot and St\'ephane Descombes and Christian Tenaud and Thierry Dumont and Violaine Louvet and Fr\'ed\'erique Laurent},
title = {New {Resolution} {Strategy} for {Multi-scale} {Reaction} {Waves} using {Time} {Operator} {Splitting} and {Space} {Adaptive} {Multiresolution:} {Application} to {Human} {Ischemic} {Stroke}},
journal = {ESAIM. Proceedings},
pages = {277--290},
year = {2011},
volume = {34},
doi = {10.1051/proc/201134006},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201134006/}
}
TY - JOUR AU - Max Duarte AU - Marc Massot AU - Stéphane Descombes AU - Christian Tenaud AU - Thierry Dumont AU - Violaine Louvet AU - Frédérique Laurent TI - New Resolution Strategy for Multi-scale Reaction Waves using Time Operator Splitting and Space Adaptive Multiresolution: Application to Human Ischemic Stroke JO - ESAIM. Proceedings PY - 2011 SP - 277 EP - 290 VL - 34 UR - http://geodesic.mathdoc.fr/articles/10.1051/proc/201134006/ DO - 10.1051/proc/201134006 LA - en ID - EP_2011_34_a6 ER -
%0 Journal Article %A Max Duarte %A Marc Massot %A Stéphane Descombes %A Christian Tenaud %A Thierry Dumont %A Violaine Louvet %A Frédérique Laurent %T New Resolution Strategy for Multi-scale Reaction Waves using Time Operator Splitting and Space Adaptive Multiresolution: Application to Human Ischemic Stroke %J ESAIM. Proceedings %D 2011 %P 277-290 %V 34 %U http://geodesic.mathdoc.fr/articles/10.1051/proc/201134006/ %R 10.1051/proc/201134006 %G en %F EP_2011_34_a6
Max Duarte; Marc Massot; Stéphane Descombes; Christian Tenaud; Thierry Dumont; Violaine Louvet; Frédérique Laurent. New Resolution Strategy for Multi-scale Reaction Waves using Time Operator Splitting and Space Adaptive Multiresolution: Application to Human Ischemic Stroke. ESAIM. Proceedings, Tome 34 (2011), pp. 277-290. doi: 10.1051/proc/201134006
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