Optimized Schwarz Methods and Model Adaptivity in Electrocardiology Simulations

Abstract

The Bidomain model is nowadays one of the most accurate mathematical descriptions of the action potential propagation in the heart. However, its numerical approximation is in general fairly expensive as a consequence of the mathematical features of this system, and several works have been devoted to devise effective solvers and preconditioners (Vigmond et al., Prog. Biophys. Mol. Biol. 96(1–3):3–18, 2008; Pennacchio and Simoncini, Appl. Numer. Math. 59(12):3033–3050, 2009), among others. A simplification of this model, called Monodomain problem is often adopted in order to reduce computational costs of the numerical solution of the cardiac potential. The latter model is however less accurate. A possible trade-off between accuracy and cost is a model adaptive strategy. The computational domain is subdivided into regions, coupled through an Optimized Schwarz Method, in which either the Bidomain or the Monodomain problem is solved, according to an a posteriori model error estimator following the spatio-temporal evolution of the action potential propagation. Here we present a possible implementation of this approach, following up previous works on the error estimation and the Optimized Schwarz coupling.