论文标题
双重自适应显式时间整合算法，用于有效求解心脏单域方程
A dual adaptive explicit time integration algorithm for efficiently solving the cardiac monodomain equation
论文作者
论文摘要
单域模型被广泛用于硅内心脏病学来描述心肌中的激发传播。通常，操作员分裂用于将单域模型中的刚性反应项和扩散项解矛，以便可以分别求解。通常，通过使用自适应时间步进的显式方法来求解反应项时，将扩散项隐含地求解。在这项工作中，我们为解耦单域模型的解提供了一种完全显式的方法。与半平式方法相反，完全显式的方法呈现出较低的记忆足迹和较高的可扩展性。但是，这种方法仅在有条件地稳定。我们通过提出一种双重自适应显式方法来克服条件稳定性限制，其中将自适应时间整合用于反应和扩散项的解决方案。在一组在生理和病理生理条件下模拟心脏传播的数值示例中，结果表明，与基于标准操作员分裂的方法相比，我们所提出的方法呈现了准确性并提高了计算效率。
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. In a set of numerical examples where cardiac propagation is simulated under physiological and pathophysiological conditions, results show that our proposed method presents preserved accuracy and improved computational efficiency as compared to standard operator splitting-based methods.
