Volume 34, December 2011Summer school on multiresolution and adaptive mesh refinement methods
|Page(s)||277 - 290|
|Published online||22 December 2011|
New Resolution Strategy for Multi-scale Reaction Waves using Time Operator Splitting and Space Adaptive Multiresolution: Application to Human Ischemic Stroke*
1 Laboratoire EM2C - UPR CNRS 288,
Ecole Centrale Paris, Grande Voie
des Vignes, 92295
e-mail: firstname.lastname@example.org, email@example.com, firstname.lastname@example.org
2 Ph.D. grant from Mathematics (INSMI) and Engineering (INSIS) Institutes of CNRS and supported by INCA project (CNRS/ONERA/SAFRAN)
3 Laboratoire J. A. Dieudonné - UMR CNRS 6621, Université de Nice - Sophia Antipolis, Parc Valrose, 06108 Nice Cedex 02, France ;
4 LIMSI - CNRS, B.P. 133, Campus d’Orsay, 91403 Orsay Cedex, France ;
5 Institut Camille Jordan - UMR CNRS 5208, Université de Lyon, Université Lyon 1, INSA de Lyon 69621, Ecole Centrale de Lyon, 43 Boulevard du 11 novembre 1918, 69622 Villeurbanne Cedex, France ;
e-mail: email@example.com, firstname.lastname@example.org
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.
Key words: Reaction-diffusion / operator splitting / adaptive multiresolution / ischemic stroke / parallel computing
This research was supported by a fundamental project grant from ANR (French National Research Agency - ANR Blancs) Séchelles (project leader S. Descombes - 2009-2013), by a CNRS PEPS Maths-ST2I project MIPAC (project leader V. Louvet - 2009-2010), and by a DIGITEO RTRA project MUSE (project leader M. Massot - 2010-2014).
© EDP Sciences, SMAI 2011
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