High-order parallel-in-time method for the monodomain equation in cardiac electrophysiology
<|reference_start|>High-order parallel-in-time method for the monodomain equation in cardiac electrophysiology: 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.<|reference_end|>
@article{de souza2024high-order,
    title={High-order parallel-in-time method for the monodomain equation in
  cardiac electrophysiology},
    author={Giacomo Rosilho de Souza, Simone Pezzuto, Rolf Krause},
    journal={arXiv preprint arXiv:2405.19994},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.19994},
    primaryClass={math.NA cs.NA}
}