发表机构
Carnegie Mellon University（卡内基梅隆大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种在中等平衡条件下的双细分六面体模板方案，首次实现所有六面体具有平面面片，并通过贪心或整数线性规划算法减少单元数，在相当单元数量下获得更高最小缩放雅可比。
AI 中文摘要
尽管六面体单元在模拟中具有数值优势，但从一般输入边界自动生成高质量且相容的六面体网格仍然是一个具有挑战性的问题。基于网格的自适应细分，随后进行悬挂节点消除，是最稳健的全自动选择。在双细分方法中，原始模板比对偶模板具有更好的网格质量，但依赖于强平衡条件，这会导致网格过度细分；两种模板系列均不能保证平面四边形面片。本文在中等平衡条件下（强平衡条件的松弛）将近期提出的原始三细分模板推广到双细分方案。32种特殊模式和五种基本模式解决了全部144种对称简化配置，随后采用快速贪心算法或整数线性规划算法，后者以额外运行时间为代价进一步减少单元数量。该方案是首个所有六面体均具有平面面片的双细分方法，其网格可直接输入到近期提出的质量保证六面体网格重建算法中。在相当的单元数量下，与三细分对应方法相比，该方法实现了相似的豪斯多夫比率和更高的最小缩放雅可比。
英文摘要
Automatically generating high-quality conforming hexahedral (hex) meshes from general input boundaries remains a challenging problem, despite the numerical advantages hex elements offer in simulation. Grid-based adaptive refinement, followed by hanging-node removal, is the most robust fully automatic choice. Among two-refinement methods, primal templates have better mesh quality than dual templates but depend on a strong balancing condition that over-refines the grid; neither family guarantees planar quadrilateral (quad) faces. This paper generalizes recent primal three-refinement templates to a two-refinement scheme under a moderate balancing condition, a relaxation of the strong one. 32 special and five fundamental patterns resolve all 144 symmetry-reduced configurations, followed by either a fast greedy algorithm or an integer linear programming (ILP) algorithm that trades extra runtime for a further reduction in element count. The scheme is the first two-refinement method in which all hexes have planar faces, and its meshes feed directly into a recent quality-guaranteed hex mesh reconstruction algorithm. At comparable element counts, it attains a similar Hausdorff ratio (HR) and a higher minimum scaled Jacobian (min SJ) than its three-refinement counterpart.
