# Optimized Schwarz Methods for the Bidomain system in electrocardiology

Luca Gerardo-Giorda; Mauro Perego

- Volume: 47, Issue: 2, page 583-608
- ISSN: 0764-583X

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topGerardo-Giorda, Luca, and Perego, Mauro. "Optimized Schwarz Methods for the Bidomain system in electrocardiology." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 47.2 (2013): 583-608. <http://eudml.org/doc/273092>.

@article{Gerardo2013,

abstract = {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.},

author = {Gerardo-Giorda, Luca, Perego, Mauro},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {domain decomposition; optimized schwarz methods; computational electrocardiology; optimized Schwarz methods},

language = {eng},

number = {2},

pages = {583-608},

publisher = {EDP-Sciences},

title = {Optimized Schwarz Methods for the Bidomain system in electrocardiology},

url = {http://eudml.org/doc/273092},

volume = {47},

year = {2013},

}

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 - Modélisation Mathématique et Analyse Numérique

PY - 2013

PB - EDP-Sciences

VL - 47

IS - 2

SP - 583

EP - 608

AB - 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.

LA - eng

KW - domain decomposition; optimized schwarz methods; computational electrocardiology; optimized Schwarz methods

UR - http://eudml.org/doc/273092

ER -

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