Efficient time splitting schemes for the monodomain equation in cardiac electrophysiology

Summary Approximating the fast dynamics of depolarization waves in the human heart described by the monodomain model is numerically challenging. Splitting methods for the PDE-ODE coupling enable the computation with very ﬁne space and time discretizations. Here, we compare diﬀerent splitting approaches regarding convergence, accuracy and eﬃciency. Simulations were performed for a benchmark conﬁguration with the Beeler–Reuter cell model on a truncated ellipsoid approximating the left ventricle including a localized stimulation. For this benchmark conﬁguration, we provide a reference solution for the transmembrane potential. We found a semi-implicit approach with state variable interpolation to be the most eﬃcient scheme. The results are transferred to a more physiological setup using a bi-ventricular domain with a complex external stimulation pattern to evaluate the accuracy of the activation time for diﬀerent resolutions in space and time. total the ionic current interpolation (ICI) state variable interpolation (SVI), semi-implicit time component-wise ICI Lagrange interpolation of the total ionic current, the SVI the the L 2 tests of the approximation variants the cell at quadrature evaluated diﬀerent lumping variants and the eﬀect of the mesh size on properties such as the conduction velocity of the depolarization wave. We conﬁrm the diﬀerence of the approximations by ICI and SVI on the anatomically relevant electrophysiology benchmark setup, and we extend the investigation to a full time and space convergence study. We show that the reaction-diﬀusion splitting has the same numerical behavior as the ICI ansatz it was in we show that a component-wise splitting method with SVI is more than the reaction-diﬀusion splitting or component-wise splitting combined with ICI. that the stability of component-wise splitting is considerably improved by the Lagrange interpolation in the PDE-ODE coupling by the L 2 projection. The smoothness of the external current in space and time has a strong inﬂuence on the convergence properties for the transmembrane voltage, the results from the benchmark conﬁguration are extended to realistic bi-ventricular setting, the convergence in space and activation semi-implicit