Efficient algebraic solution of reaction-diffusion systems for the cardiac excitation process.

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.