A model preconditioner for the Bidomain problem in electrocardiology

We introduce a preconditioner for the solution of the Bidomain system governing the propagation of action potentials in the myocardial tissue, represented by a degenerate parabolic set of nonlinear reaction-diffusion equations. The nonlinear term describes the ion flux at the cellular level. The degenerate nature of the problem results in a severe ill conditioning of its discretization. Our preconditioning strategy is based on a suitable adaptation of the Monodomain model, a simplified version of the Bidomain one, which is by far simpler to solve, nevertheless is unable to capture significant features of the action potential propagation. We prove optimality for the preconditioner with respect to the mesh size, and corroborate our results with 3D numerical simulations. ∗ Corresponding author. Email addresses: [email protected] (L. Gerardo-Giorda),