Parallel and space-time adaptivity for the numerical simulation of cardiac action potentials

Abstract

In this work, the study of parallel and space-time adaptivity for the numerical simulation of action potential propagation in cardiac electrophysiology is presented. The monodomain and bidomain models are employed for the numerical realization. This work is devoted to investigate the spatial adaptivity which is realized within multi finite element methods by using a gradient type a posteriori error estimator and the temporal adaptivity determined by a linearly implicit time integration techniques. In addition, the parallelization of such space-time adaptivity for the simulation of spiral wave dynamics based on non-overlapping domain decomposition techniques and dynamic load balancing is discussed. The numerical results demonstrate that the parallel simulations have been accelerated reasonably good using the adaptive space and time algorithm, with no significant loss in accuracy, for the single action potential wave propagation as well as reentry situations.