Journal
APPLIED NUMERICAL MATHEMATICS
Volume 59, Issue 12, Pages 3033-3050Publisher
ELSEVIER
DOI: 10.1016/j.apnum.2009.08.001
Keywords
Reaction-diffusion system; Iterative methods; Algebraic multigrid; Preconditioning
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The so-called bidomain system is possibly the most complete model for the cardiac bioelectric activity. It consists of a reaction-diffusion system, modeling the intra, extracellular and transmembrane potentials, coupled through a nonlinear reaction term with a stiff system of ordinary differential equations describing the ionic Currents through the cellular membrane. In this paper we address the problem of efficiently solving the large linear system arising in the finite element discretization of the bidomain model, when a semiimplicit method in time is employed. We analyze the use of structured algebraic multigrid preconditioners on two major formulations of the model, and report on our numerical experience under different discretization parameters and various discontinuity properties of the conductivity tensors. Our numerical results show that the less exercised formulation provides the best overall performance on a typical Simulation of the myocardium excitation process. (C) 2009 IMACS. Published by Elsevier B.V. All rights reserved.
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