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Linear dependence of bivariate Minimal Support and Locally Refined B-splines over LR-meshes

Linear dependence of bivariate Minimal Support and Locally Refined B-splines over LR-meshes

Category
Journal publication
Abstract
The focus on locally refined spline spaces has grown rapidly in recent years due to the need in Isogeometric Analysis (IgA) of spline spaces with local adaptivity: a property not offered by the strict regular structure of tensor product B-spline spaces. However, this flexibility sometimes results in collections of B-splines spanning the space that are not linearly independent. In this paper we address the minimal number of Minimal Support B-splines (MS B-splines) and of Locally Refined B-splines (LR B-splines) that can form a linear dependence relation. We show that such minimal numbers are six for MS B-splines and eight for LR B-splines. Further results are established to help detecting collections of B-splines that are linearly independent.
Language
English
Author(s)
Affiliation
  • SINTEF Digital / Mathematics and Cybernetics
  • University of Oslo
Year
2019
Published in
Computer Aided Geometric Design
ISSN
0167-8396
Volume
77