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.

翻译：单域方程的模拟对于心脏电活动建模至关重要，当传统数值方法仅在空间维度并行化时，其可扩展性面临限制。为通过更有效地分配计算负载来优化大型多处理器计算机的使用，时间并行化必不可少。我们提出了一种高阶时间并行方法，以应对心脏动力学所具有的刚性、多尺度和非线性特性带来的重大计算挑战。该方法结合了半隐式与指数谱延迟校正方法，形成了一种混合方法，并利用PFASST框架扩展至时间并行。我们通过大量数值实验，使用如ten-Tusscher-Panfilov等实际离子模型，全面评估了所提时间并行方法的稳定性、精度和鲁棒性。结果突显了该方法在生物医学研究和临床应用中显著提升实时性与高保真模拟的潜力。