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.

翻译：全显式稳定多速率（mRKC）方法凭借其增强的稳定性特性，非常适合求解刚性常微分方程的大型多尺度系统。为验证该方法在求解刚性、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，我们提出了一种针对单域模型优化的改进版本，即显式指数多速率稳定（emRKC）方法。通过考虑不同有限元网格（结构化和非结构化）及真实离子模型，进行了多组数值实验以评估mRKC和emRKC方法的效率。新型emRKC方法在心脏电生理学计算中通常优于标准的隐式-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方法在保持精度的同时具有更快的计算速度和固有的并行性。