Contributed Talk
Efficient IMEX and Implicit Methods for 3D Cardiac Reaction-Diffusion Models
Department of Mathematics, University of Pavia, Italy
Abstract
We construct and study IMEX and implicit methods for the time discretization of cardiac reaction-diffusion models in three dimensions, which couple a system of stiff ordinary differential equations with a system of parabolic partial differential equations (PDEs). We consider time discretizations ranging from the simple implicit Euler scheme to linearly implicit Rosenbrock schemes, integrated with decoupled and operator-splitting techniques, using both fixed and adaptive time-step strategies. The nonlinear systems arising at each time step of the implicit discretizations are solved using scalable Newton-Krylov-Schwarz methods based on overlapping additive Schwarz techniques. Several parallel numerical results in three dimensions confirm the convergence rates predicted by theory and evaluate the performance of our algorithms over a complete heartbeat for different cardiac reaction-diffusion models. The results demonstrate a considerable CPU-time reduction when using decoupled Schwarz solvers compared to fully implicit Schwarz solvers. Finally, we present the application of these solvers to the study of re-entry induction and cardiac arrhythmogenesis.
This is joint work with Simone Scacchi, Marilena Munteanu, Ngoc Monica Mai Huynh.