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Optimized Schwarz Methods for the Bidomain system inelectrocardiology

Published online by Cambridge University Press:  18 January 2013

Luca Gerardo-Giorda  and
Mauro Perego
Luca Gerardo-Giorda
Affiliation:
BCAM, Basque Center for Applied Mathematics, Bilbao, Spain.. lgerardo@bcamath.org
Mauro Perego
Affiliation:
Dept. of Scientific Computing, The Florida State University, Thallahassee, FL, USA.; mperego@fsu.edu
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Abstract

The propagation of the action potential in the heart chambers is accurately described bythe Bidomain model, which is commonly accepted and used in the specialistic literature.However, its mathematical structure of a degenerate parabolic system entails highcomputational costs in the numerical solution of the associated linear system. Domaindecomposition methods are a natural way to reduce computational costs, and OptimizedSchwarz Methods have proven in the recent years their effectiveness in accelerating theconvergence of such algorithms. The latter are based on interface matching conditions moreefficient than the classical Dirichlet or Neumann ones. In this paper we analyze anOptimized Schwarz approach for the numerical solution of the Bidomain problem. We assessthe convergence of the iterative method by means of Fourier analysis, and we investigatethe parameter optimization in the interface conditions. Numerical results in 2D and 3D aregiven to show the effectiveness of the method.

Keywords

Domain decompositionoptimized schwarz methodscomputational electrocardiology
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 2 , March 2013 , pp. 583 - 608
Copyright
© EDP Sciences, SMAI, 2013

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