  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.
