High-order parallel-in-time method for the monodomain equation in cardiac electrophysiology
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909213339418624 |
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| author | de Souza, Giacomo Rosilho Pezzuto, Simone Krause, Rolf |
| author_facet | de Souza, Giacomo Rosilho Pezzuto, Simone Krause, Rolf |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_19994 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | High-order parallel-in-time method for the monodomain equation in cardiac electrophysiology de Souza, Giacomo Rosilho Pezzuto, Simone Krause, Rolf Numerical Analysis 65L04, 65L10, 65L20, 65Y05 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. |
| title | High-order parallel-in-time method for the monodomain equation in cardiac electrophysiology |
| topic | Numerical Analysis 65L04, 65L10, 65L20, 65Y05 |
| url | https://arxiv.org/abs/2405.19994 |