Cantwell Chris D, Yakovlev Sergey, Kirby Robert M, Peters Nicholas S, Sherwin Spencer J
National Heart and Lung Institute, Imperial College London, London, UK.
School of Computing and Scientific Computing and Imaging (SCI) Institute, Univ. of Utah, Salt Lake City, UT, USA.
J Comput Phys. 2014 Jan 15;257(PA):813-829. doi: 10.1016/j.jcp.2013.10.019.
We present a numerical discretisation of an embedded two-dimensional manifold using high-order continuous Galerkin spectral/ elements, which provide exponential convergence of the solution with increasing polynomial order, while retaining geometric flexibility in the representation of the domain. Our work is motivated by applications in cardiac electrophysiology where sharp gradients in the solution benefit from the high-order discretisation, while the computational cost of anatomically-realistic models can be significantly reduced through the surface representation and use of high-order methods. We describe and validate our discretisation and provide a demonstration of its application to modelling electrochemical propagation across a human left atrium.
我们提出了一种使用高阶连续伽辽金谱元对嵌入二维流形进行数值离散化的方法，该方法随着多项式阶数的增加能实现解的指数收敛，同时在域的表示中保持几何灵活性。我们的工作受到心脏电生理学应用的推动，在该领域中，解中的陡峭梯度得益于高阶离散化，而通过表面表示和使用高阶方法，解剖学真实模型的计算成本可以显著降低。我们描述并验证了我们的离散化方法，并展示了其在模拟电化学在人左心房中的传播方面的应用。
