This paper presents a subdivision scheme for unstructured quadrilateral meshes with improved convergence rates in extraordinary regions for isogeometric analysis compared with that of Catmull–Clark and related tuned subdivision schemes. The new subdivision stencils are first constructed to ensure C¹ continuity with bounded curvature at extraordinary positions. The eigenbasis functions corresponding to the subsubdominant eigenvalues are further optimized towards standard quadratics of the corresponding characteristic maps using the remaining degrees of freedom plus necessary constraints in meeting other desired properties. We verify the convergence rate of the subdivision scheme by approximating known target functions of field solutions in comparison with that obtained using Catmull–Clark and other tuned subdivision schemes. The results show that the convergence rates obtained in terms of the L² norm are consistent with the optimal convergence rate of cubic spline patches in regular regions of the subdivision scheme.

本文提出了一种非结构四边形网格的细分方案，与Catmull–Clark和相关的调优细分方案相比，该方案在非常规区域具有更高的收敛速度，可用于等几何分析。首先构造新的细分模具以确保C ¹在非凡位置具有有限曲率的连续性。使用剩余的自由度加上满足其他所需特性的必要约束，将对应于次主要特征值的特征基础函数进一步优化为对应特征图的标准二次方。通过与使用Catmull–Clark和其他调整后的细分方案获得的目标函数进行比较，我们通过逼近野外解决方案的已知目标函数来验证细分方案的收敛速度。结果表明，以L ²范数表示的收敛速度与细分方案规则区域中三次样条斑块的最优收敛速度一致。