Spline Upwind for space-time Isogeometric Analysis of cardiac electrophysiology

Paola F. Antonietti, Luca Dedè, Gabriele Loli, Giancarlo Sangalli, Paolo Tesini

Abstract: This work proposes a stabilized space--time method for the monodomain equation coupled with the Rogers--McCulloch ionic model, which is widely used to simulate electrophysiological wave propagation in the cardiac tissue. By extending the Spline Upwind method and exploiting low-rank matrix approximations, as well as preconditioned solvers, we achieve both significant computational efficiency and accuracy. In particular, we develop a formulation that is both simple and highly effective, designed to minimize spurious oscillations and ensuring computational efficiency. We rigorously validate the method's performance through a series of numerical experiments, showing its robustness and reliability in diverse scenarios.