An approximation scheme for the anisotropic and nonlocal mean curvature flow
An approximation scheme for the anisotropic and nonlocal mean curvature flow
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各向异性非局部平均曲率流的近似方案
DOI：
10.1007/s00030-013-0244-z
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Katsuyuki Ishii
中科院分区：
文献类型：
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作者：
梶原 毅;綿谷安男;Katsuyuki Ishii
2004年Chambolle提出了一种基于变分问题的平均曲率流算法。此后，他的算法的收敛、扩展和应用得到了很多人的研究。在本文中，我们使用有符号距离函数证明了 Chambolle 算法各向异性版本的收敛性。还讨论了我们的方案在非局部曲率流（例如晶体曲率流）的近似中的应用。
In 2004 Chambolle proposed an algorithm for mean curvature flow based on a variational problem. Since then, the convergence, extensions and applications of his algorithm have been studied by many people. In this paper we give a proof of the convergence of an anisotropic version of Chambolle’s algorithm by use of the signed distance function. An application of our scheme to an approximation of the nonlocal curvature flow such as crystalline one is also discussed.