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

Micol Pennacchio () and Valeria Simoncini ()
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Micol Pennacchio: Istituto di Matematica Applicata e Tecnologie Informatiche del CNR
Valeria Simoncini: Università di Bologna, Dipartimento di Matematica

A chapter in Numerical Mathematics and Advanced Applications 2009, 2010, pp 729-736 from Springer

Abstract: 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.

Keywords: Conductivity Tensor; Saddle Point Problem; Eigenvector Matrix; Bidomain Model; Exact Case (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/978-3-642-11795-4_78

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