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

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

2 Scopus Citations
View graph of relations

Author(s)

Related Research Unit(s)

Detail(s)

Original languageEnglish
Article number101043
Journal / PublicationGraphical Models
Volume106
Online published14 Sep 2019
Publication statusPublished - Nov 2019

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.

Research Area(s)

  • Bounded curvature, IGA, Isogeometric analysis, Optimal convergence rate, Subdivision scheme