Optimal Rate of Convergence of the Bence-Merriman-Osher Algorithm for Motion by Mean Curvature
Optimal Rate of Convergence of the Bence-Merriman-Osher Algorithm for Motion by Mean Curvature
复制标题
DOI：
10.1137/04061862x
复制
发表时间：
2005
期刊：
影响因子：
--
通讯作者：
K. Ishii
中科院分区：
文献类型：
--
作者：
K. Ishii
Bence， Merriman和Osher提出了一种计算超曲面运动的算法，该算法根据通常的热方程的解计算平均曲率，在短时间步长后不断重新初始化。本文利用Allen—Cahn方程的渐近分析技巧，给出了其算法在光滑紧致超曲面上的平均曲率运动的收敛速率。我们还考虑了圆按曲率演化的特殊情况，并证明了我们的速率是最优的。
Bence, Merriman, and Osher proposed an algorithm for computing the motion a hypersurface by mean curvature in terms of solutions of the usual heat equation, continually reinitialized after short time steps. In this paper, applying some techniques of asymptotic analysis for the Allen--Cahn equation, we give a rate of convergence of their algorithm for the motion of a smooth and compact hypersurface by mean curvature. We also consider the special case of a circle evolving by curvature and show that our rate is optimal.