It is well known that numerical simulations of the cardiac monodomain model require fine mesh resolution, which increases the computational resources required. In this paper, we construct three operator-splitting alternating direction implicit (ADI) schemes to efficiently solve the nonlinear cardiac monodomain model. The main objective of the proposed methods is to reduce the computational time and memory consumed for solving electrocardiology models, compared to standard numerical methods. The proposed methods have second-order accuracy in both space and time while evaluating the ionic model only once per time-step. Several examples using regular wave, spiral wave reentry, and nonsymmetrical scroll wave are conducted, and the efficiency of the proposed ADI methods is compared to the standard semi-implicit Crank–Nicolson/Adams–Bashforth method. Large-scale two- and three-dimensional simulations are performed.

众所周知，心脏单畴模型的数值模拟需要精细的网格分辨率，这增加了所需的计算资源。在本文中，我们构造了三种算子分解交替方向隐式（ADI）方案，以有效地解决非线性心脏单畴模型。与标准数值方法相比，提出的方法的主要目的是减少用于求解心电图模型的计算时间和内存消耗。所提出的方法在空间和时间上均具有二阶精度，而每个时间步仅评估一次离子模型。进行了几个使用规则波，螺旋波折返和非对称涡旋波的示例，并将拟议的ADI方法的效率与标准的半隐式Crank–Nicolson / Adams–Bashforth方法进行了比较。