# New Resolution Strategy for Multi-scale Reaction Waves using Time Operator Splitting and Space Adaptive Multiresolution: Application to Human Ischemic Stroke*

Max Duarte; Marc Massot; Stéphane Descombes; Christian Tenaud; Thierry Dumont; Violaine Louvet; Frédérique Laurent

ESAIM: Proceedings (2011)

- Volume: 34, page 277-290
- ISSN: 1270-900X

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topDuarte, Max, et al. Louvet, Violaine, and Massot, Marc, eds. "New Resolution Strategy for Multi-scale Reaction Waves using Time Operator Splitting and Space Adaptive Multiresolution: Application to Human Ischemic Stroke*." ESAIM: Proceedings 34 (2011): 277-290. <http://eudml.org/doc/251232>.

@article{Duarte2011,

abstract = {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. },

author = {Duarte, Max, Massot, Marc, Descombes, Stéphane, Tenaud, Christian, Dumont, Thierry, Louvet, Violaine, Laurent, Frédérique},

editor = {Louvet, Violaine, Massot, Marc},

journal = {ESAIM: Proceedings},

keywords = {Reaction-diffusion; operator splitting; adaptive multiresolution; ischemic stroke; parallel computing; reaction-diffusion},

language = {eng},

month = {12},

pages = {277-290},

publisher = {EDP Sciences},

title = {New Resolution Strategy for Multi-scale Reaction Waves using Time Operator Splitting and Space Adaptive Multiresolution: Application to Human Ischemic Stroke*},

url = {http://eudml.org/doc/251232},

volume = {34},

year = {2011},

}

TY - JOUR

AU - Duarte, Max

AU - Massot, Marc

AU - Descombes, Stéphane

AU - Tenaud, Christian

AU - Dumont, Thierry

AU - Louvet, Violaine

AU - Laurent, Frédérique

AU - Louvet, Violaine

AU - Massot, Marc

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

DA - 2011/12//

PB - EDP Sciences

VL - 34

SP - 277

EP - 290

AB - 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.

LA - eng

KW - Reaction-diffusion; operator splitting; adaptive multiresolution; ischemic stroke; parallel computing; reaction-diffusion

UR - http://eudml.org/doc/251232

ER -

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