用于心脏电生理学中单域模型的显式稳定多速率方法
Explicit stabilized multirate methods for the monodomain model in cardiac electrophysiology
AI总结：
本研究针对心脏电生理学单域方程的数值求解问题，提出定制化的显式指数多速率稳定（emRKC）方法，经多组数值实验验证，该方法比标准隐式-显式基准方法更高效，并行性强且不损失精度。
摘要：
全显式稳定多速率（mRKC）方法凭借其更优的稳定特性，非常适合求解刚性常微分方程的大型多尺度系统的数值解。为了验证其在求解刚性、多尺度非线性抛物型偏微分方程数值解方面的效率，我们将mRKC方法应用于心脏电生理学中的单域方程。在此过程中，我们提出了一种专门针对单域模型定制的改进版本，由此得到显式指数多速率稳定（emRKC）方法。我们开展了多项数值实验来评估mRKC和emRKC的效率，实验中考虑了不同的有限元网格（结构化和非结构化）以及符合实际的离子模型。新型emRKC方法的表现通常优于心脏电生理学领域的标准隐式-显式基准方法。代码性能分析和强可扩展性结果进一步表明，emRKC速度更快，具备固有的并行性，且不会牺牲精度。
英文摘要：
Fully explicit stabilized multirate (mRKC) methods are well-suited for the numerical solution of large multiscale systems of stiff ordinary differential equations thanks to their improved stability properties. To demonstrate their efficiency for the numerical solution of stiff, multiscale, nonlinear parabolic PDE's, we apply mRKC methods to the monodomain equation from cardiac electrophysiology. In doing so, we propose an improved version, specifically tailored to the monodomain model, which leads to the explicit exponential multirate stabilized (emRKC) method. Several numerical experiments are conducted to evaluate the efficiency of both mRKC and emRKC, while taking into account different finite element meshes (structured and unstructured) and realistic ionic models. The new emRKC method typically outperforms a standard implicit-explicit baseline method for cardiac electrophysiology. Code profiling and strong scalability results further demonstrate that emRKC is faster and inherently parallel without sacrificing accuracy.
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