Istituto di Matematica Applicata e Tecnologie Informatiche     
Pennacchio M., Simoncini V. Efficient algebraic solution of reaction-diffusion systems for the cardiac excitation process. Preprint ercim.cnr.ian//2000-1189, 2000.
In this paper we deal with the problem of solving the large algebraic linear system arising in the numerical solution of a reaction-diffusion (R-D) system associated with myocardial excitation process modeling. We show that an ad-hoc preconditioning technique can be devised so as to efficiently and simultaneously handle the differential equations of the R--D system, with no additional memory requirements. Two different formulations are commonly considered for the theoretical and numerical analyses, respectively. We observe that the formulation employed for the theoretical analysis of the problem actually yields the best numerical performance, when compared with the usual numerical scheme.
Subject Reaction-diffusion system, iterative methods, preconditioning
65F10, 65F15, 35K57, 35K65

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