The propagation of the action potential in the heart chambers is accurately described by the Bidomain model, which is commonly accepted and used in the specialistic literature. However, its mathematical structure of a degenerate parabolic system entails high computational costs in the numerical solution of the associated linear system. Domain decomposition methods are a natural way to reduce computational costs, and Optimized Schwarz Methods have proven in the recent years their effectiveness in accelerating the convergence of such algorithms. The latter are based on interface matching conditions more efficient than the classical Dirichlet or Neumann ones. In this paper we analyze an Optimized Schwarz approach for the numerical solution of the Bidomain problem. We assess the convergence of the iterative method by means of Fourier analysis, and we investigate the parameter optimization in the interface conditions. Numerical results in 2D and 3D are given to show the effectiveness of the method.
Mots clés : domain decomposition, optimized schwarz methods, computational electrocardiology
@article{M2AN_2013__47_2_583_0,
author = {Gerardo-Giorda, Luca and Perego, Mauro},
title = {Optimized {Schwarz} {Methods} for the {Bidomain} system in electrocardiology},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {583--608},
publisher = {EDP-Sciences},
volume = {47},
number = {2},
year = {2013},
doi = {10.1051/m2an/2012040},
mrnumber = {3021699},
zbl = {1274.92021},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2012040/}
}
TY - JOUR AU - Gerardo-Giorda, Luca AU - Perego, Mauro TI - Optimized Schwarz Methods for the Bidomain system in electrocardiology JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2013 SP - 583 EP - 608 VL - 47 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2012040/ DO - 10.1051/m2an/2012040 LA - en ID - M2AN_2013__47_2_583_0 ER -
%0 Journal Article %A Gerardo-Giorda, Luca %A Perego, Mauro %T Optimized Schwarz Methods for the Bidomain system in electrocardiology %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2013 %P 583-608 %V 47 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2012040/ %R 10.1051/m2an/2012040 %G en %F M2AN_2013__47_2_583_0
Gerardo-Giorda, Luca; Perego, Mauro. Optimized Schwarz Methods for the Bidomain system in electrocardiology. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 47 (2013) no. 2, pp. 583-608. doi : 10.1051/m2an/2012040. http://www.numdam.org/articles/10.1051/m2an/2012040/
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