We present a new explicit local space-time adaptive framework to decrease the time required for monodomain simulations for cardiac electrophysiology. Based on the localized structure of the steep activation wavefront in solutions to monodomain problems, the proposed framework adopts small time steps and a tree-based adaptive mesh refinement scheme only in the regions necessary to resolve these localized structures. The time step and mesh adaptation selection process is fully controlled by a combination of local error indicators. The main contributions of this work consist in the introduction of a primal symmetric interior penalty formulation of the monodomain model and an efficient algorithmic strategy to manage local time stepping for its temporal discretization. In a first serial implementation of this framework, we report decreases in wall-clock time between 2 and 20 times with respect to an optimized implementation of a commonly used numerical scheme, showing that this framework is a promising candidate to accelerate monodomain simulations of cardiac electrophysiology.

翻译：我们提出了一种新的显式局部时空自适应框架，以减少心脏电生理单域模拟所需的时间。基于单域问题解中陡峭激活波前的局部化结构，所提出的框架仅在需要解析这些局部化结构的区域采用小时间步长和基于树的自适应网格细化方案。时间步长和网格自适应选择过程完全由局部误差指示器的组合控制。本工作的主要贡献包括引入单域模型的原始对称内罚变分形式，以及一种高效的算法策略来管理其时间离散化的局部时间步长。在该框架的首个串行实现中，与常用数值方案的优化实现相比，我们报告了墙钟时间减少2到20倍，表明该框架是加速心脏电生理单域模拟的一个有前景的候选方案。