CORRADO, Cesare; LASSOUED, Jamila; MAHJOUB, Moncef; ZEMZEMI, Nejib

doi:10.1016/j.mbs.2015.12.005

Métadonnées

Licence d’utilisation du document

CORRADO, Cesare
Modélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]

LASSOUED, Jamila
Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis] [LR-LAMSIN-ENIT]

MAHJOUB, Moncef
Université de Tunis El Manar [UTM]
Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis] [LR-LAMSIN-ENIT]

Langue

Article de revue

Ce document a été publié dans

Mathematical Biosciences. 2015-12-04

Elsevier

Résumé en anglais

In this work we show the numerical stability of the Proper Orthogonal Decomposition (POD) reduced order method used in cardiac electrophysiology applications. The difficulty of proving the stability comes from the fact that we are interested in the bidomain model, which is a system of degenerate parabolic equations coupled to a system of ODEs representing the cell membrane electrical activity. The proof of the stability of this method is based an a priori estimate controlling the gap between the reduced order solution and the Galerkin finite element one. We present some numerical simulations confirming the theoretical results. We also combine the POD method with a time splitting scheme allowing a faster solution of the bidomain problem and show numerical results. Finally, we conduct numerical simulation in 2D illustrating the stability of the POD method in its sensitivity to the ionic model parameters. We also perform 3D simulation using a massively parallel code. We show the computational gain using the POD reduced order model. We also show that this method has a better scalability than the full finite element method.< Réduire

Mots clés en anglais

proper orthogonal decomposition

reduced order method

Bidomain equation

a priori estimates

ionic parameters

stability analysis

Mitchell-Schaeffer model

URI

https://oskar-bordeaux.fr/handle/20.500.12278/194241

DOI

http://dx.doi.org/10.1016/j.mbs.2015.12.005

Project ANR

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