Rocha Bernardo Martins, Dos Santos Rodrigo Weber, Igreja Iury, Loula Abimael F D
Computer Science Department and Computational Modeling Graduate Program, Federal University of Juiz de Fora, Juiz de Fora, Brazil.
National Laboratory of Scientific Computing, Petrópolis, Brazil.
Int J Numer Method Biomed Eng. 2020 Jul;36(7):e3341. doi: 10.1002/cnm.3341. Epub 2020 May 8.
Numerical methods for solving the cardiac electrophysiology model, which describes the electrical activity in the heart, are proposed. The model problem consists of a nonlinear reaction-diffusion partial differential equation coupled to systems of ordinary differential equations that describes electrochemical reactions in cardiac cells. The proposed methods combine an operator splitting technique for the reaction-diffusion equation with primal hybrid methods for spatial discretization considering continuous or discontinuous approximations for the Lagrange multiplier. A static condensation is adopted to form a reduced global system in terms of the multiplier only. Convergence studies exhibit optimal rates of convergence and numerical experiments show that the proposed schemes can be more efficient than standard numerical techniques commonly used in this context when preconditioned iterative methods are used for the solution of linear systems.
提出了用于求解描述心脏电活动的心脏电生理模型的数值方法。该模型问题由一个非线性反应扩散偏微分方程与描述心脏细胞中电化学反应的常微分方程组耦合而成。所提出的方法将反应扩散方程的算子分裂技术与用于空间离散化的原始混合方法相结合，其中考虑了拉格朗日乘子的连续或间断近似。采用静态凝聚仅根据乘子形成一个简化的全局系统。收敛性研究展示了最优收敛速率，数值实验表明，当使用预处理迭代方法求解线性系统时，所提出的格式比在此背景下常用的标准数值技术更有效。
