Space–time Isogeometric Analysis of Cardiac Electrophysiology
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In our work, we propose 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 cardiac tissue. By extending the Spline Upwind method, that generalizes classical upwinding, as SUPG, to higher degree splines, and leveraging low-rank matrix approximations along with preconditioned solvers, we achieve significant improvements in both computational efficiency and accuracy. Our formulation is designed to be both simple and highly effective, minimizing spurious oscillations while ensuring numerical stability and performance. Furthermore, we validate the proposed method through a series of numerical experiments in both 2D and 3D spatial domains, corresponding to 3D and 4D space–time domains, respectively, demonstrating its robustness and reliability across various scenarios.