Direct Approach to Mean-curvature Flow with Topological Changes
Direct Approach to Mean-curvature Flow with Topological Changes
复制标题
拓扑变化平均曲率流的直接方法
作者：
P. Paus;M. Beneš
这一贡献涉及位错动力学的数值模拟。位错可以用一族闭合或开放的光滑曲线Γ（t）：S → S ~ 2，t ~ 0的演化来描述。曲线由法向速度ν驱动，法向速度ν是曲率κ和位置的函数。演化规律为：ν = -κ + F。运动规律用直接法处理，数值求解用两种格式，例如，向后欧拉半隐半离散直线法。通过对曲线点进行切向重分布，提高了数值稳定性，从而使计算时间更长，精度更高。位错动力学模拟的结果（e。例如，在一个实施例中，沟道或Frank-Read源中的位错）。我们还介绍了一种算法，用于处理拓扑变化的演变曲线。
This contribution deals with the numerical simulation of dislocation dynamics. Dislocations are described by means of the evolution of a family of closed or open smooth curves Γ(t): S → ℝ 2 , t ≧ 0. The curves are driven by the normal velocity ν which is the function of curvature κ and the position. The evolution law reads as: ν = -κ + F. The motion law is treated using direct approach numerically solved by two schemes, i. e., backward Euler semi-implicit and semi-discrete method of lines. Numerical stability is improved by tangential redistribution of curve points which allows long time computations and better accuracy. The results of dislocation dynamics simulation are presented (e. g., dislocations in channel or Frank-Read source). We also introduce an algorithm for treatment of topological changes in the evolving curve.