Second order threshold dynamics schemes for two phase motion by mean curvature
Second order threshold dynamics schemes for two phase motion by mean curvature
复制标题
平均曲率两相运动的二阶阈值动力学方案
DOI：
10.1016/j.jcp.2020.109404
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发表时间：
2020
影响因子：
4.1
通讯作者：
Garikipati, Krishna
中科院分区：
文献类型：
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作者：
Zaitzeff, Alexander;Esedoḡlu, Selim;Garikipati, Krishna
Merriman、Bence 和 Osher 的阈值动力学算法在两相设置中仅具有一阶精度。在多相设置中，其精度进一步降低到半阶，这是它与其他相关的更新算法（例如 Voronoi 隐式界面方法的等表面张力版本）所共有的缺点。作为解决这一缺点的第一步，我们提出了两相阈值动力学的两个不同的二阶精确版本。与之前在这个方向上的努力不同，我们为我们的两种算法提供了仔细的一致性计算。第一种算法在任何空间维度上都与其二阶极限（平均曲率运动）一致。第二种仅在二维上实现二阶精度，但在任何维度上都具有严格的稳定性保证（无条件能量稳定性）——这在同类高阶方案中尚属首次。
The threshold dynamics algorithm of Merriman, Bence, and Osher is only first order accurate in the two-phase setting. Its accuracy degrades further to half order in the multi-phase setting, a shortcoming it has in common with other related, more recent algorithms such as the equal surface tension version of the Voronoi implicit interface method. As a first, rigorous step in addressing this shortcoming, we present two different second order accurate versions of two-phase threshold dynamics. Unlike in previous efforts in this direction, we present careful consistency calculations for both of our algorithms. The first algorithm is consistent with its limit (motion by mean curvature) up to second order in any space dimension. The second achieves second order accuracy only in dimension two, but comes with a rigorous stability guarantee (unconditional energy stability) in any dimension – a first for high order schemes of its type.