In mesoscopic scale microstructure evolution modeling, two primary numerical frameworks are used: Front-Capturing (FC) and Front-Tracking (FT) ones. FC models, like phase-field or level-set methods, indirectly define interfaces by tracking field variable changes. On the contrary, FT models explicitly define interfaces using interconnected segments or surfaces. In historical FT methodologies, Vertex models were first developed and consider the description of the evolution of polygonal structures in terms of the motion of points where multiple boundaries meet. Globally, FT-type approaches, often associated with Lagrangian movement, enhance spatial resolution in 3D surfacic and 2D lineic problems using techniques derived from finite element meshing and remeshing algorithms. These efficient approaches, by nature, are well adapted to physical mechanisms correlated to interface properties and geometries. They also face challenges in managing complex topological events, especially in 3D. However, recent advances highlight their potential in computational efficiency and analysis of mobility and energy properties, with possible applications in intragranular phenomena.

翻译：在介观尺度微观结构演化建模中，主要采用两种数值框架：前沿捕获（FC）与前沿追踪（FT）方法。FC模型（如相场法或水平集方法）通过追踪场变量的变化间接定义界面。相反，FT模型使用相互连接的线段或曲面显式定义界面。在历史发展的FT方法中，顶点模型最先被提出，其通过追踪多条边界交汇点的运动来描述多边形结构的演化。总体而言，FT类方法常与拉格朗日运动相关联，通过采用源自有限元网格生成与重网格算法的技术，在三维曲面与二维线状问题中提升了空间分辨率。这些高效方法本质上非常适用于与界面属性及几何形态相关的物理机制。然而，它们在处理复杂拓扑事件（尤其在三维情况下）时仍面临挑战。尽管如此，最新进展凸显了其在计算效率、迁移率与能量特性分析方面的潜力，并可能应用于晶内现象的研究。