A subdivision scheme for unstructured quadrilateral meshes with improved convergence rate for isogeometric analysis

Abstract

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.