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Algebraic multigrid preconditioners for the bidomain reaction-diffusion system. (English) Zbl 1171.92017
Summary: 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.
We address the problem of efficiently solving the large linear system arising in the finite element discretization of the bidomain model, when a semi-implicit 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.

MSC:
92C30 Physiology (general)
92C05 Biophysics
35K57 Reaction-diffusion equations
37N25 Dynamical systems in biology
34A34 Nonlinear ordinary differential equations and systems, general theory
Software:
HSL_MI20; Matlab; PIFISS
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References:
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