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

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. 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.
Complete list of metadatas

Cited literature [20 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00590812
Contributor : Max Duarte <>
Submitted on : Saturday, May 7, 2011 - 1:36:52 PM
Last modification on : Thursday, November 21, 2019 - 2:24:18 AM
Long-term archiving on : Friday, November 9, 2012 - 10:55:11 AM

File

Duarte_etal_ESAIM.pdf
Files produced by the author(s)

Identifiers

Citation

Max Duarte, Marc Massot, Stéphane Descombes, Christian Tenaud, Thierry Dumont, et al.. New Resolution Strategy for Multi-scale Reaction Waves using Time Operator Splitting and Space Adaptive Multiresolution: Application to Human Ischemic Stroke. E. Cancès, V. Louvet, M. Massot. Summer school on multiresolution and adaptive mesh refinement methods, EDP Sciences, pp.Vol. 34 277-290, 2011, ESAIM: Proceedings, ⟨10.1051/proc/201134006⟩. ⟨hal-00590812⟩

Share

Metrics

Record views

1674

Files downloads

370