基于结晶 eikonal-curvature flow 演化螺旋的 ODE 方法与 level set method 的数值分析比较
Numerical analysis comparing ODE approach and level set method for evolving spirals by crystalline eikonal-curvature flow
AI总结：
本文比较了固定中心结晶曲率流演化多边形螺旋曲线的ODE离散模型与level set method，通过计算包围区域面积的归一化L1范数发现两种模型数值结果差异极小。
摘要：
本文从两个视角考虑了具有固定中心的结晶曲率流驱动的多边形螺旋曲线的演化，这两个视角分别是包含面长度ODE系统的离散模型和level set method。我们通过计算这些螺旋曲线所包围区域的面积，在数值上研究了这些模型之间的差异。面积差异通过阶跃函数的归一化L1范数来计算，这些阶跃函数是arg(x)的分支，其不连续点仅位于螺旋上。我们发现，尽管这些模型在中心和最远面附近的演化规律略有不同，但本文考虑的数值结果差异非常小。
英文摘要：
In this paper, the evolution of a polygonal spiral curve by the crystalline curvature flow with a pinned center is considered with two view points, discrete model consist of an ODE system of facet lengths and a level set method. We investigate the difference of these models numerically by calculating the area of the region enclosed by these spiral curves. The area difference is calculated by the normalized L1 norm of the difference of step-like functions which are branches of arg(x) whose discontinuities are only on the spirals. We find the differences of the numerical results considered in this paper are very small even though the evolution laws of these models around the center and the farthest facet are slightly different.
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