Hierarchical bases of spline spaces with highest order smoothness over hierarchical T-subdivisions

Authors:
Meng Wu;Jinlan Xu;Ruimin Wang;Zhouwang Yang
Affiliations:
School of Mathematical Sciences, University of Science and Technology of China, China;School of Mathematical Sciences, University of Science and Technology of China, China;School of Mathematical Sciences, University of Science and Technology of China, China;School of Mathematical Sciences, University of Science and Technology of China, China
Venue:
Computer Aided Geometric Design
Year:
2012

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Abstract

The prospect of applying spline spaces over T-subdivisions to adaptive isogeometric analysis is an exciting one. One major issue with spline spaces over T-subdivisions is in providing proper bases (shape functions) for finite element analysis. In this paper, we propose a method for the construction of hierarchical bases of a spline space with highest order smoothness over a consistent hierarchical T-subdivision. Our method is induced by the surjection condition, and this set of basis functions is hierarchically adaptive. We also present a concrete set of non-negative hierarchical bases over a T-subdivision and apply them in adaptive finite element analysis.