| Issue |
ESAIM: M2AN
Volume 58, Number 6, November-December 2024
Special issue - To commemorate Assyr Abdulle
|
|
|---|---|---|
| Page(s) | 2225 - 2254 | |
| DOI | https://doi.org/10.1051/m2an/2024030 | |
| Published online | 04 December 2024 | |
Explicit stabilized multirate methods for the monodomain model in cardiac electrophysiology*
1
Euler Institute, Universitá della Svizzera italiana, Via G. Buffi 13, 6900 Lugano, Switzerland
2
Department of Mathematics, University of Basel, Rheinsprung 21, 4051 Basel, Switzerland
3
Laboratory for Mathematics in Biology and Medicine, Department of Mathematics, Universitá di Trento, Via Sommarive 14, 38123 Trento, Italy
4
Faculty of Mathematics and Informatics, FernUni Schweiz, Schinerstrasse 18, 3900 Brig, Switzerland
** Corresponding author: giacomo.rosilhodesouza@usi.ch
Received:
4
December
2023
Accepted:
22
April
2024
Fully explicit stabilized multirate (mRKC) methods are well-suited for the numerical solution of large multiscale systems of stiff ordinary differential equations thanks to their improved stability properties. To demonstrate their efficiency for the numerical solution of stiff, multiscale, nonlinear parabolic PDE’s, we apply mRKC methods to the monodomain equation from cardiac electrophysiology. In doing so, we propose an improved version, specifically tailored to the monodomain model, which leads to the explicit exponential multirate stabilized (emRKC) method. Several numerical experiments are conducted to evaluate the efficiency of both mRKC and emRKC, while taking into account different finite element meshes (structured and unstructured) and realistic ionic models. The new emRKC method typically outperforms a standard implicit-explicit baseline method for cardiac electrophysiology. Code profiling and strong scalability results further demonstrate that emRKC is faster and inherently parallel without sacrificing accuracy.
Mathematics Subject Classification: 65L04 / 65L06 / 65L10 / 65L20
Key words: Multirate explicit stabilized methods / Rush–Larsen / electrophysiology / monodomain model / ionic model / local time-stepping
© The authors. Published by EDP Sciences, SMAI 2024
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