Algebraic multigrid preconditioners for the bidomain reaction--diffusion system

  • Authors:

  • Micol Pennacchio;Valeria Simoncini

  • Affiliations:

  • Istituto di Matematica Applicata e Tecnologie Informatiche del C.N.R., via Ferrata, 1, 27100 Pavia, Italy;Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato, 5, I-40127 Bologna, Italy and CIRSA, Ravenna and IMATI-CNR, Pavia, Italy

  • Venue:
  • Applied Numerical Mathematics
  • Year:
  • 2009

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Abstract

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.