An unconditionally stable threshold dynamics method for the Willmore flow

被引：0
作者：
Shengqing Hu
Zijie Lin
Dong Wang
Xiao-Ping Wang
机构：
[1] The Chinese University of Hong Kong,School of Science and Engineering
[2] University of Utah,Department of Mathematics
[3] Shenzhen Research Institute of Big Data,Shenzhen International Center for Industrial and Applied Mathematics
[4] The Hong Kong University of Science and Technology,Department of Mathematics
来源：
Japan Journal of Industrial and Applied Mathematics | 2023年 / 40卷
关键词：
Willmore flow; Threshold dynamics method; Gaussian kernel;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we propose a threshold dynamics method for the Willmore flow with a new kernel constructed based on the combination of a Gaussian kernel and a Cosine function. We show the consistency of the method by asymptotic analysis and construct a Lyapunov functional to show the unconditional stability of the proposed method. Compare to previous work, no artificial parameters are required for the construction of the kernel. Numerical experiments including area preservation or perimeter preservation are performed to show the effectiveness of the method.
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页码：1519 / 1546
页数：27
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共 98 条
[1]  
Bao W(2017)A parametric finite element method for solid-state Dewetting problems with anisotropic surface energies J. Comput. Phys. 330 380-400
[2]  
Jiang W(1995)A simple proof of convergence for an approximation scheme for computing motions by mean curvature SIAM J. Numer. Anal. 32 484-500
[3]  
Wang Y(2012)Consistency result for a non monotone scheme for anisotropic mean curvature flow Interfaces Free Bound. 14 1-35
[4]  
Zhao Q(2006)Convergence of an algorithm for the anisotropic and crystalline mean curvature flow SIAM J. Math. Anal. 37 1978-1987
[5]  
Barles G(2005)A phase field formulation of the Willmore problem Nonlinearity 18 1249-1267
[6]  
Georgelin C(2004)A phase field approach in the numerical study of the elastic bending energy for vesicle membranes J. Comput. Phys. 198 450-468
[7]  
Bonnetier E(2006)Simulating the deformation of vesicle membranes under elastic bending energy in three dimensions J. Comput. Phys. 212 757-777
[8]  
Bretin E(2017)Threshold dynamics for anisotropic surface energies Math. Comput. 87 1721-1756
[9]  
Chambolle A(2015)Threshold dynamics for networks with arbitrary surface tensions Commun. Pure Appl. Math. 68 808-864
[10]  
Chambolle A(2006)Threshold dynamics for the piecewise constant Mumford–Shah functional J. Comput. Phys. 211 367-384
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