High-order parallel-in-time method for the monodomain equation in cardiac electrophysiology

TL;DR

This paper presents a high-order parallel-in-time numerical method for the monodomain equation in cardiac electrophysiology, enabling more efficient simulations of the heart's electrical activity on large multi-processor systems.

Contribution

It introduces a novel hybrid semi-implicit and exponential spectral deferred correction method extended with PFASST for parallel-in-time computation of cardiac models.

Findings

Enhanced stability and accuracy demonstrated through numerical experiments.

Significant potential for real-time cardiac simulation applications.

Effective handling of stiff, multiscale, and nonlinear dynamics.

Abstract

Simulation of the monodomain equation, crucial for modeling the heart's electrical activity, faces scalability limits when traditional numerical methods only parallelize in space. To optimize the use of large multi-processor computers by distributing the computational load more effectively, time parallelization is essential. We introduce a high-order parallel-in-time method addressing the substantial computational challenges posed by the stiff, multiscale, and nonlinear nature of cardiac dynamics. Our method combines the semi-implicit and exponential spectral deferred correction methods, yielding a hybrid method that is extended to parallel-in-time employing the PFASST framework. We thoroughly evaluate the stability, accuracy, and robustness of the proposed parallel-in-time method through extensive numerical experiments, using practical ionic models such as the ten-Tusscher-Panfilov. The results underscore the method's potential to significantly enhance real-time and high-fidelity simulations in biomedical research and clinical applications.