Computational analysis of the conserved curvature driven flow for open curves in the plane
Computational analysis of the conserved curvature driven flow for open curves in the plane
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平面内开曲线守恒曲率驱动流的计算分析
DOI：
10.1016/j.matcom.2016.02.004
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
D. Ševčovič
中科院分区：
文献类型：
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作者：
M. Kolár;M. Beneš;D. Ševčovič
本文用数值方法研究了具有固定端点的平面开放曲线的约束曲率流。这一定律起源于晶体材料的相变理论，它描述了封闭嵌入曲线在恒定封闭面积下的演化。我们证明，对于具有固定端点的开放曲线，该区域也是保留的。在这里，面积是由曲线和它的两端连接到坐标原点给出的。我们给出了任何其他解在时间上渐近收敛到的定常解的形式。用直接法将演化规律转化为退化抛物型偏微分方程组，实现曲线的参数化。该方程组采用流动有限体积法进行空间离散，并用显式龙格-库塔法进行数值求解。我们通过我们的数值数据和已知的解析解，实验地研究了该格式的逼近阶。我们还讨论了合适的切向重分布的作用。为此，提出了几个与开放曲线动力学相关的计算研究。
The paper studies the constrained curvature flow for open planar curves with fixed endpoints by means of its numerical solution. This law originates in the theory of phase transitions for crystalline materials and where it describes the evolution of closed embedded curves with constant enclosed area. We show that the area is preserved for open curves with fixed endpoints as well. Here, the area is given by the curve and its ends connected to the origin of coordinates. We provide the form of the stationary solution towards which any other solution converges asymptotically in time. The evolution law is reformulated by means of the direct method into the system of degenerate parabolic partial differential equations for the curve parametrization. This system is spatially discretized by means of the flowing finite volumes method and solved numerically by the explicit Runge–Kutta solver. We experimentally investigate the order of approximation of the scheme by means of our numerical data and by knowing the analytical solution. We also discuss the role of the suitable tangential redistribution. For this purpose, several computational studies related to the open curve dynamics are presented.
DOI：
--
发表时间：
2007-12
期刊：
arXiv: Numerical Analysis
影响因子：
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作者：
M. Beneš;M. Kimura;P. Paus;D. Ševčovič;T. Tsujikawa;S. Yazaki
通讯作者：
M. Beneš;M. Kimura;P. Paus;D. Ševčovič;T. Tsujikawa;S. Yazaki