COUDIÈRE, Yves; DOUANLA LONTSI, Charlie; PIERRE, Charles

doi:10.1016/j.matcom.2018.04.006

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COUDIÈRE, Yves
Institut de Mathématiques de Bordeaux [IMB]
Modélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]

DOUANLA LONTSI, Charlie
Institut de Mathématiques de Bordeaux [IMB]
Modélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]

PIERRE, Charles
Laboratoire de Mathématiques et de leurs Applications [Pau] [LMAP]

Langue

Article de revue

Ce document a été publié dans

Mathematics and Computers in Simulation. 2018, vol. 153, p. 15-34

Elsevier

Résumé en anglais

Models in cardiac electrophysiology are coupled systems of reaction diffusion PDE and of ODE. The ODE system displays a very stiff behavior. It is non linear and its upgrade at each time step is a preponderant load in the computational cost. The issue is to develop high order explicit and stable methods to cope with this situation.In this article, is is analyzed the resort to exponential Adams Bashforth (EAB) integrators in cardiac electrophysiology. The method is presented in the framework of a general and varying stabilizer, that is well suited in this context. Stability under perturbation (or 0-stability) is proven. It provides a new approach for the convergence analysis of the method. The Dahlquist stability properties of the method is performed. It is presented in a new framework that incorporates the discrepancy between the stabilizer and the system Jacobian matrix. Provided this discrepancy is small enough, the method is shown to be A(alpha)-stable. This result is interesting for an explicit time-stepping method. Numerical experiments are presented for two classes of stiff models in cardiac electrophysiology. They include performances comparisons with several classical methods. The EAB method is observed to be as stable as implicit solvers and cheaper at equal level of accuracy.< Réduire

Mots clés en anglais

explicit high-order multistep methods

stiff equations

Dahlquist stability

exponential integrators of Adams type

stability and convergence

URI

https://oskar-bordeaux.fr/handle/20.500.12278/193315

DOI

http://dx.doi.org/10.1016/j.matcom.2018.04.006

Project ANR

Modèles numériques haute résolution de l'électrophysiologie cardiaque - ANR-13-MONU-0004
L'Institut de Rythmologie et modélisation Cardiaque - ANR-10-IAHU-0004

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251