A dynamic mesh algorithm for curvature dependent evolving interfaces
A dynamic mesh algorithm for curvature dependent evolving interfaces
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DOI：
10.1006/jcph.1996.0025
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发表时间：
1996-02-01
影响因子：
4.1
通讯作者：
Verdi, C
中科院分区：
文献类型：
--
作者：
Nochetto, RH;Paolini, M;Verdi, C
本文讨论了一种新的有限元方法来逼近R（n）中法向速度等于平均曲率加一个强迫函数的演化界面。该方法是不敏感的奇异性形成，并保留了局部结构的极限问题，因此，表现出典型的R（n-1）的计算复杂性，而不具有缺点的前端跟踪策略。一个渐变的动态网格周围的传播前是唯一的分区存在于任何时间步，是显着小于一个完整的网格。时间步进是明确的，但稳定性约束迫使小的时间步长只有当奇点发展，而相对较大的时间步长之前或过去的奇点，当演化是平滑的。显式推进方案还保证了每个时间步最多只能添加或删除一层元素，从而使网格更新简单，因此实用。性能和潜力通过2D、3D、4D和8D的数值模拟以及轴对称性得到充分证明。它们包括平均曲率流的环面和锥面，具有给定边界的最小和预定平均曲率曲面，光滑驱动力的增肥，以及体积约束。(C)出版社：Academic Press，Inc.
A new finite element method is discussed for approximating evolving interfaces in R(n) whose normal velocity equals mean curvature plus a forcing function. The method is insensitive to singularity formation and retains the local structure of the limit problem and, thus, exhibits a computational complexity typical of R(n-1) without having the drawbacks of front-tracking strategies. A graded dynamic mesh around the propagating front is the sole partition present at any time step and is significantly smaller than a full mesh. Time stepping is explicit, but stability constraints force small time steps only when singularities develop, whereas relatively large time steps are allowed before or past singularities, when the evolution is smooth. The explicit marching scheme also guarantees that at most one layer of elements has to be added or deleted per time step, thereby making mesh updating simple and, thus, practical. Performance and potentials are fully documented via a number of numerical simulations in 2D, 3D, 4D, and 8D, with axial symmetries. They include tori and cones for the mean curvature flow, minimal and prescribed mean curvature surfaces with given boundary, fattening for smooth driving force, and volume constraint. (C) 1996 Academic Press, Inc.