The locality of solution features in cardiac electrophysiology simulations calls for adaptive methods. Due to the overhead incurred by established mesh refinement and coarsening, however, such approaches failed in accelerating the computations. Here we investigate a different route to spatial adaptivity that is based on nested subset selection for algebraic degrees of freedom in spectral deferred correction methods. This combination of algebraic adaptivity and iterative solvers for higher order collocation time stepping realizes a multirate integration with minimal overhead. This leads to moderate but significant speedups in both monodomain and cell-by-cell models of cardiac excitation, as demonstrated at four numerical examples.

翻译：心脏电生理模拟中解特征的局部性要求采用自适应方法。然而，由于传统网格细化与粗化产生额外开销，此类方法未能有效加速计算。本文探索了一种基于谱延迟校正方法中代数自由度嵌套子集选择的空间自适应新路径。这种代数自适应性与高阶配置时间步进迭代求解器的结合，以最小开销实现了多速率积分。四个数值算例表明，该方法在心脏兴奋的单域模型与逐细胞模型中均实现了适度但显著的计算加速。