Planar-faced and high-Jacobian two-refinement hexahedral templates

2026-09-13

AI Summary

本文提出了一种新的两步细化六面体网格生成方法，通过中等平衡条件和ILP算法，解决了高质量六面体网格自动生成的问题，保证了所有六面体具有平面面。

Abstract

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.

Problem

• hexahedral mesh
• planar faces
• two-refinement
• high-quality mesh
• adaptive refinement

Innovation

• two-refinement
• planar faces
• moderate balancing condition
• integer linear programming (ILP)
• minimum scaled Jacobian (min SJ)