论文标题
部分可观测时空混沌系统的无模型预测
A structure-preserving numerical method for the fourth-order geometric evolution equations for planar curves
论文作者
论文摘要
对于平面曲线的四阶几何进化方程，包括弯曲能的耗散，包括Willmore和Helfrich流，我们考虑了一种数值方法。在这项研究中，我们基于离散的衍生化方法构建了一种结构性的方法。此外，为了防止可能导致数值不稳定的顶点浓度，我们离散地引入了Deckelnick的切向速度。在这里，在添加切向速度的过程中引入了修改项。该修改术语使该方法可以在防止顶点浓度的同时重现方程的属性。数值实验表明，所提出的方法以高精度捕获了方程的特性，并避免了顶点的浓度。
For fourth-order geometric evolution equations for planar curves with the dissipation of the bending energy, including the Willmore and the Helfrich flows, we consider a numerical approach. In this study, we construct a structure-preserving method based on a discrete variational derivative method. Furthermore, to prevent the vertex concentration that may lead to numerical instability, we discretely introduce Deckelnick's tangential velocity. Here, a modification term is introduced in the process of adding tangential velocity. This modified term enables the method to reproduce the equations' properties while preventing vertex concentration. Numerical experiments demonstrate that the proposed approach captures the equations' properties with high accuracy and avoids the concentration of vertices.
