Numerical quadrature and operator splitting in finite element methods for cardiac electrophysiology
Numerical quadrature and operator splitting in finite element methods for cardiac electrophysiology
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DOI：
10.1002/cnm.2573
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发表时间：
2013-11-01
影响因子：
2.1
通讯作者：
Klug, William S.
中科院分区：
文献类型：
--
作者：
Krishnamoorthi, Shankarjee;Sarkar, Mainak;Klug, William S.
我们研究了心脏电生理单域方程的有限元解过程的替代公式的数值精度和计算效率，重点是空间正交实现与算子分裂的相互作用，并检查了节点和高斯正交方法以及将状态变量的节点存储与高斯正交混合的实现。我们评估了一致电容和质量矩阵的集总近似的所有可能组合的性能。最普遍的是，我们发现产生解耦节点离子方程的正交方案和集中近似允许最大的计算效率，这是通过使用离子状态变量ode的异步自适应时间步进来提供的。我们确定了两种具有优越精度的集总近似方案，可与最昂贵的可变一致性实现相媲美。最后，我们说明了与心律失常和纤颤相关的电生理模拟中离散误差的一些生理后果。这些结果表明，在使用大多数商用网格划分软件中可用的半自动自由形式四面体和六面体网格划分算法时要谨慎，这些算法会产生具有较大元素尺寸分布的非均匀网格。版权所有：John Wiley & Sons， Ltd。
We study the numerical accuracy and computational efficiency of alternative formulations of the finite element solution procedure for the monodomain equations of cardiac electrophysiology, focusing on the interaction of spatial quadrature implementations with operator splitting and examining both nodal and Gauss quadrature methods and implementations that mix nodal storage of state variables with Gauss quadrature. We evaluate the performance of all possible combinations of lumped' approximations of consistent capacitance and mass matrices. Most generally, we find that quadrature schemes and lumped approximations that produce decoupled nodal ionic equations allow for the greatest computational efficiency, this being afforded through the use of asynchronous adaptive time-stepping of the ionic state variable ODEs. We identify two lumped approximation schemes that exhibit superior accuracy, rivaling that of the most expensive variationally consistent implementations. Finally, we illustrate some of the physiological consequences of discretization error in electrophysiological simulation relevant to cardiac arrhythmia and fibrillation. These results suggest caution with the use of semi-automated free-form tetrahedral and hexahedral meshing algorithms available in most commercially available meshing software, which produce nonuniform meshes having a large distribution of element sizes. Copyright (c) 2013 John Wiley & Sons, Ltd.