考虑体效应的阈值格式的收敛性
Convergence of thresholding schemes incorporating bulk effects
摘要：
在本文中，我们建立了三个计算算法的收敛性的界面运动的多相系统，其中包括体积效应。考虑的算法属于阈值方案的分类，在著名的Merriman-Bence-Osher算法的精神，用于产生由中曲率移动的界面。这里考虑的方案都包括来自体积中能量的局部力，或来自体积约束的非局部力。我们首先建立了一个方案的收敛性Ruuth-Wetton提出的近似保体积平均曲率流。接下来，我们研究了由表面张力加上体积能量产生的几何流的方案。这里的极限是运动的中曲率（MMC）加上强迫项。第三，我们考虑了一个阈值计划模拟晶粒生长的多晶周围的空气，其中包括固-气界面上的边界效应。在晶界上的极限流动是MMC，在固-气界面上的极限流动是保体积MMC。
英文摘要：
In this paper we establish the convergence of three computational algorithms for interface motion in a multi-phase system, which incorporate bulk effects. The algorithms considered fall under the classification of thresholding schemes, in the spirit of the celebrated Merriman-Bence-Osher algorithm for producing an interface moving by mean curvature. The schemes considered here all incorporate either a local force coming from an energy in the bulk, or a non-local force coming from a volume constraint. We first establish the convergence of a scheme proposed by Ruuth-Wetton for approximating volume-preserving mean-curvature flow. Next we study a scheme for the geometric flow generated by surface tension plus bulk energy. Here the limit is motion by mean curvature (MMC) plus forcing term. Third we consider a thresholding scheme for simulating grain growth in a polycrystal surrounded by air, which incorporates boundary effects on the solid-vapor interface. The limiting flow is MMC on the inner grain boundaries, and volume-preserving MMC on the solid-vapor interface.
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