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Comparison study for Level set and Direct Lagrangian methods for computing Willmore flow of closed planar curves

机译:水平集和直接拉格朗日方法计算闭合平面曲线的Willmore流的比较研究

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The main goal of this paper is to present results of comparison study for the level set and direct Lagrangian methods for computing evolution of the Willmore flow of embedded planar curves. To perform such a study we construct new numerical approximation schemes for both Lagrangian as well as level set methods based on semi-implicit in time and finite/complementary volume in space discretizations. The Lagrangian scheme is stabilized in tangential direction by the asymptotically uniform grid point redistribution. Both methods are experimentally second order accurate. Moreover, we show precise coincidence of both approaches in case of various elastic curve evolutions provided that solving the linear systems in semi-implicit level setrnmethod is done in a precise way, redistancing is performed occasionally and the influence of boundary conditions on the level set function is eliminated.
机译:本文的主要目的是提供水平集和直接拉格朗日方法的比较研究结果,该方法用于计算嵌入式平面曲线的Willmore流的演化。为了进行这样的研究,我们基于时间的半隐式和空间离散化中的有限/互补体积,为拉格朗日方法和水平集方法构造了新的数值逼近方案。拉格朗日方案通过渐近均匀的网格点重新分布在切线方向上稳定。两种方法在实验上都是二阶准确的。而且,如果以精确的方式解决半隐式水平设定方法中的线性系统,偶尔进行重新分配以及边界条件对水平设定函数的影响,则在各种弹性曲线演化的情况下,我们展示了两种方法的精确一致性。被淘汰。

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