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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

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Sammendrag
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.
Språk
Engelsk
Forfatter(e)
Institusjon(er)
  • SINTEF Digital / Mathematics and Cybernetics
  • Universitetet i Oslo
År
2019
Publisert i
Computer Aided Geometric Design
ISSN
0167-8396
Årgang
77