Adaptive Multiresolution Methods for the Simulation of Waves in Excitable Media

Détails

ID Serval
serval:BIB_F8C528A32B66
Type
Article: article d'un périodique ou d'un magazine.
Collection
Publications
Titre
Adaptive Multiresolution Methods for the Simulation of Waves in Excitable Media
Périodique
Journal of Scientific Computing
Auteur(s)
Bürger R., Ruiz-Baier R., Schneider K.
ISSN-L
0885-7474
Statut éditorial
Publié
Date de publication
2010
Peer-reviewed
Oui
Volume
43
Pages
261-290
Langue
anglais
Résumé
We present fully adaptive multiresolution methods for a
class of spatially two-dimensional reaction-diffusion
systems which describe excitable media and often give
rise to the formation of spiral waves. A novel model
ingredient is a strongly degenerate diffusion term that
controls the degree of spatial coherence and serves as a
mechanism for obtaining sharper wave fronts. The
multiresolution method is formulated on the basis of two
alternative reference schemes, namely a classical finite
volume method, and Barkleyâeuro?s approach (Barkley in Phys. D
49:61--70, 1991), which consists in separating the
computation of the nonlinear reaction terms from that of
the piecewise linear diffusion. The proposed methods are
enhanced with local time stepping to attain local
adaptivity both in space and time. The computational
efficiency and the numerical precision of our methods are
assessed. Results illustrate that the fully adaptive
methods provide stable approximations and substantial
savings in memory storage and CPU time while preserving
the accuracy of the discretizations on the corresponding
finest uniform grid.
Mots-clé
Spiral waves, Adaptive multiresolution scheme, Finite, volume approximation, Aliev-Panfilov model
Création de la notice
02/07/2013 10:54
Dernière modification de la notice
03/03/2018 22:52
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