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Non-Symmetric Algebraic Multigrid Preconditioners for the Bidomain Reaction–Diffusion system

In: Numerical Mathematics and Advanced Applications 2009

Author

Listed:
  • Micol Pennacchio

    (Istituto di Matematica Applicata e Tecnologie Informatiche del CNR)

  • Valeria Simoncini

    (Università di Bologna, Dipartimento di Matematica
    IMATI-CNR)

Abstract

We deal with the efficient solution of the so-called bidomain system which is possibly the most complete model for the cardiac bioelectric activity. We study the performance of a non-symmetric structured algebraic multigrid (AMG) preconditioner on the formulation generally used of the bidomain model, i.e., the one characterized by a parabolic equation coupled with an elliptic one. Our numerical results show that, for this formulation, the non-symmetric preconditioner provides the best overall performance compared with the AMG based block structured preconditioners developed in [J. Sci. Comput. 36, 391–419 (2008)]. In this paper we provide theoretical justification for the observed optimality.

Suggested Citation

  • Micol Pennacchio & Valeria Simoncini, 2010. "Non-Symmetric Algebraic Multigrid Preconditioners for the Bidomain Reaction–Diffusion system," Springer Books, in: Gunilla Kreiss & Per Lötstedt & Axel Målqvist & Maya Neytcheva (ed.), Numerical Mathematics and Advanced Applications 2009, pages 729-736, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-11795-4_78
    DOI: 10.1007/978-3-642-11795-4_78
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