An adaptive hybridizable discontinuous Galerkin approach for cardiac electrophysiology
An adaptive hybridizable discontinuous Galerkin approach for cardiac electrophysiology
复制标题
用于心脏电生理学的自适应杂交不连续伽辽金方法
DOI：
10.1002/cnm.2959
复制
发表时间：
2018
影响因子：
2.1
通讯作者：
W. Wall
中科院分区：
文献类型：
--
作者：
Julia Hoermann;C. Bertoglio;M. Kronbichler;M. Pfaller;R. Chabiniok;W. Wall
心脏电生理学模拟在数值上具有挑战性，因为陡峭的电化学波前的传播，因此需要用小网格尺寸进行离散化以获得准确的结果。在这项工作中，我们提出了一种基于可杂交不连续Galerkin方法（HDG）的方法，该方法允许将高阶离散化有效地实现到计算框架中。特别地，利用不连续函数空间的优势，我们提出了一种有效的p-自适应策略来精确跟踪波前。HDG允许将最终线性系统中的总体自由度减少到仅在元件界面上的自由度。此外，我们提出了一个规则，离子电流项的适当的积分精度取决于多项式的阶数和细胞模型来处理高阶多项式。我们的结果表明，对于相同的自由度，粗高阶单元比细低阶单元提供更精确的结果。引入p自适应进一步降低了计算成本，同时通过限制使用高阶元素来解析波前来保持精度。对于心动周期的患者特定模拟，与非自适应模型相比，p自适应将平均自由度减少了95%。除了降低计算成本外，使用粗糙网格和我们的p自适应高阶HDG方法还简化了网格生成和后处理的实际方面。
Cardiac electrophysiology simulations are numerically challenging because of the propagation of a steep electrochemical wave front and thus require discretizations with small mesh sizes to obtain accurate results. In this work, we present an approach based on the hybridizable discontinuous Galerkin method (HDG), which allows an efficient implementation of high‐order discretizations into a computational framework. In particular, using the advantage of the discontinuous function space, we present an efficient p‐adaptive strategy for accurately tracking the wave front. The HDG allows to reduce the overall degrees of freedom in the final linear system to those only on the element interfaces. Additionally, we propose a rule for a suitable integration accuracy for the ionic current term depending on the polynomial order and the cell model to handle high‐order polynomials. Our results show that for the same number of degrees of freedom, coarse high‐order elements provide more accurate results than fine low‐order elements. Introducing p‐adaptivity further reduces computational costs while maintaining accuracy by restricting the use of high‐order elements to resolve the wave front. For a patient‐specific simulation of a cardiac cycle, p‐adaptivity reduces the average number of degrees of freedom by 95% compared to the nonadaptive model. In addition to reducing computational costs, using coarse meshes with our p‐adaptive high‐order HDG method also simplifies practical aspects of mesh generation and postprocessing.
DOI：
10.1016/j.physrep.2014.05.002
发表时间：
2014-10-10
期刊：
Physics reports
影响因子：
--
作者：
Qu Z;Hu G;Garfinkel A;Weiss JN
通讯作者：
Weiss JN
模拟可压缩流的高阶稳定有限元方法性能分析
影响因子：
7.2
作者：
Sevilla R
通讯作者：
Sevilla R