The monodomain model is widely used in in-silico cardiology to describe excitation propagation in the myocardium. Frequently, operator splitting is used to decouple the stiff reaction term and the diffusion term in the monodomain model so that they can be solved separately. Commonly, the diffusion term is solved implicitly with a large time step while the reaction term is solved by using an explicit method with adaptive time stepping. In this work, we propose a fully explicit method for the solution of the decoupled monodomain model. In contrast to semi-implicit methods, fully explicit methods present lower memory footprint and higher scalability. However, such methods are only conditionally stable. We overcome the conditional stability limitation by proposing a dual adaptive explicit method in which adaptive time integration is applied for the solution of both the reaction and diffusion terms. We perform a set of numerical examples where cardiac propagation is simulated under physiological and pathophysiological conditions. Results show that the proposed method presents preserved accuracy and improved computational efficiency as compared to standard operator splitting-based methods.

中文翻译：

---

一种有效求解心脏单域方程的双自适应显式时间积分算法

单域模型广泛应用于in-silico心脏病学来描述心肌中的兴奋传播。通常，算子分裂用于解耦单域模型中的刚性反应项和扩散项，以便它们可以单独求解。通常，扩散项使用大时间步长隐式求解，而反应项使用具有自适应时间步长的显式方法求解。在这项工作中，我们提出了一种完全显式的方法来解决解耦的单域模型。与半隐式方法相比，全显式方法具有更低的内存占用和更高的可扩展性。然而，这样的方法只是条件稳定的。我们通过提出一种双自适应显式方法来克服条件稳定性限制，其中自适应时间积分应用于反应和扩散项的解决方案。我们执行一组数值示例，其中在生理和病理生理条件下模拟心脏传播。结果表明，与标准的基于算子分裂的方法相比，所提出的方法具有保留的准确性和提高的计算效率。