移动边界问题的全离散曲线缩短多边形演化律
A fully discrete curve-shortening polygonal evolution law for moving boundary problems
摘要：
本文研究了具有曲线缩短性质的移动边界问题的数值积分，如中曲率流和Hele-Shaw流。我们提出了一个完全离散的曲线缩短多边形演化规律。所提出的演化规律是完全隐式的，推导的关键是以隐式方式设计每个顶点处的切向和法向量以及切向和法向速度的定义。数值实验表明，该方法允许使用相对较大的时间步长，也捕捉到了良好的精度的面积保持或耗散属性。
英文摘要：
We consider the numerical integration of moving boundary problems with the curve-shortening property, such as the mean curvature flow and Hele-Shaw flow. We propose a fully discrete curve-shortening polygonal evolution law. The proposed evolution law is fully implicit, and the key to the derivation is to devise the definitions of tangent and normal vectors and tangential and normal velocities at each vertex in an implicit manner. Numerical experiments show that the proposed method allows the use of relatively large time step sizes and also captures the area-preserving or dissipative property in good accuracy.
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