In this paper, the evolution of a polygonal spiral curve by the crystalline curvature flow with a pinned center is considered from two viewpoints; a discrete model consisting of an ODE system describing facet lengths and another using level set method. We investigate the difference of these models numerically by calculating the area of an interposed region by their spiral curves. The area difference is calculated by the normalized $ L^1 $ norm of the difference of step-like functions which are branches of $ \arg (x) $ whose discontinuities are on the spirals. We find that the differences in the numerical results are small, even though the model equations around the center and the farthest facet are slightly different.

中文翻译：

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晶体固有曲率流演化螺旋的ODE数值分析和能级集方法

在本文中，从两个角度考虑了具有固定中心的曲率流对多边形螺旋曲线的演化。一个离散模型，由描述刻面长度的ODE系统和另一个使用级别集方法组成的模型组成。我们通过计算它们的螺旋曲线通过计算插入区域的面积来数值研究这些模型的差异。面积差是通过阶梯状函数之差的归一化$ L ^ 1 $范数计算的，这些函数是不连续在螺旋上的$ \ arg（x）$的分支。我们发现，即使围绕中心和最远小平面的模型方程式稍有不同，数值结果的差异也很小。