论文标题
无振荡的完全分区方案，用于心脏活动力学的数值建模
An oscillation-free fully partitioned scheme for the numerical modeling of cardiac active mechanics
论文作者
论文摘要
在心电机电的硅模型中，将描述不同物理学的数学模型俩融合在一起。一个实例由描述活性力产生的模型，以及一种组织力学。对于耦合模型的数值解，经常使用两个子问题的顺序解的分区方案。但是，这种方法可能是不稳定的。因此，耦合模型通常以高计算成本的价格使用牛顿类型算法作为独特的系统解决。鉴于这种动机，在本文中，我们提出了一种新的数值方案，该方案在数字上稳定且准确，但在一个完全分区（即隔离）框架内。具体而言，我们介绍了标准分离方案（一个数值一致的稳定项），能够消除常用隔离方案的数值解中存在的非物理振荡。我们的新方法是从基于物理学的分析对力产生动力学的显微镜能量学分析。通过考虑主动力学的模型问题，我们证明了所提出的方案是无条件绝对稳定的（即，对于任何时间步长的稳定），与标准分离的方案不同，我们还提供将方案作为分数步骤方法的解释。我们通过几个数值测试表明，提出的稳定项成功地消除了表征非稳定分离隔离方案解决方案的非物理数值振荡。我们的数值测试是针对文献中可用的几种力量产生模型进行的，即Niederer-Hunter-Smith模型，土地和同事的模型以及我们最近提出的平均场力产生模型。最后，我们应用了建议的方案[...]
In silico models of cardiac electromechanics couple together mathematical models describing different physics. One instance is represented by the model describing the generation of active force, coupled with the one of tissue mechanics. For the numerical solution of the coupled model, partitioned schemes, that foresee the sequential solution of the two subproblems, are often used. However, this approach may be unstable. For this reason, the coupled model is commonly solved as a unique system using Newton type algorithms, at the price, however, of high computational costs. In light of this motivation, in this paper we propose a new numerical scheme, that is numerically stable and accurate, yet within a fully partitioned (i.e. segregated) framework. Specifically, we introduce, with respect to standard segregated scheme, a numerically consistent stabilization term, capable of removing the nonphysical oscillations otherwise present in the numerical solution of the commonly used segregated scheme. Our new method is derived moving from a physics-based analysis on the microscale energetics of the force generation dynamics. By considering a model problem of active mechanics we prove that the proposed scheme is unconditionally absolutely stable (i.e. it is stable for any time step size), unlike the standard segregated scheme, and we also provide an interpretation of the scheme as a fractional step method. We show, by means of several numerical tests, that the proposed stabilization term successfully removes the nonphysical numerical oscillations characterizing the non stabilized segregated scheme solution. Our numerical tests are carried out for several force generation models available in the literature, namely the Niederer-Hunter-Smith model, the model by Land and coworkers, and the mean-field force generation model that we have recently proposed. Finally, we apply the proposed scheme [...]
