Non-symmetric algebraic multigrid preconditioners for the bidomain reaction-diffusion system

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.