基于水平集网格演化方法的二维开放曲线的贴合跟踪
Body-fitted tracking of 2d open curves with a level set based mesh evolution method
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中文总结 AI 辅助
研究二维开放曲线运动跟踪算法，结合曲线显式网格化与水平集方法隐式捕获的互补表示，可进行精确几何或机械计算，用于模拟涡旋片卷起等，还能优化曲线形状以改善激光轨迹或重建断裂集。
中文摘要 AI 辅助
本文描述了一种用于跟踪二维空间中一组开放曲线运动的新型数值算法。所提出的策略在演化过程的每次迭代中结合了这些曲线的两种互补表示：一方面，将它们显式网格化，作为整个计算域网格实体的子集合。同时，使用水平集方法的变体，将它们隐式捕获为在整个环境空间上定义的两个辅助标量函数的负、零和正子集的代数组合。这种表示的耦合允许对这些曲线进行精确的几何或机械计算，同时为其形状的大演化留出空间。在描述了其主要数值要素之后，提出了该方法的几个应用示例，用于模拟开放物理不连续性（如涡旋片卷起）的运动，以及优化开放曲线的形状（如关于其各向异性长度），以改善增材制造中作用于粉末床的激光轨迹或重建断裂集。
英文摘要
This article describes a novel numerical algorithm for tracking the motion of a collection of open curves in two space dimensions. The proposed strategy combines two complementary representations of these curves at each iteration of the evolution process: on the one hand, they are meshed explicitly, as a sub-collection of the entities of a mesh of the total computational domain. Concurrently, using a variant of the Level Set Method, they are captured implicitly as algebraic combinations of the negative, zero and positive subsets of two auxiliary scalar functions, defined on the whole ambient space. This coupling of representations allows to perform accurate geometric or mechanical computations on these curves, while leaving room for large evolution of their shape. After the description of its main numerical ingredients, several applications examples of this methodology are proposed, where it is used to simulate the motion of open physical discontinuities, such as a vortex sheet roll-up, and to optimize the shape of open-ended curves, e.g. with respect to their anisotropic length, with the aim to improve the trajectory of a laser acting on a powder bed in the context of additive manufacturing, or to reconstruct fracture sets.
