Year: 2015
Author: Xin Li
Journal of Computational Mathematics, Vol. 33 (2015), Iss. 4 : pp. 428–442
Abstract
Analysis-suitable $T$-splines (AS $T$-splines) are a mildly topological restricted subset of T-splines which are linear independent regardless of knot values [1–3]. The present paper provides some more iso-geometric analysis (IGA) oriented properties for AS $T$-splines and generalizes them to arbitrary topology AS $T$-splines. First, we prove that the blending functions for analysis-suitable T-splines are locally linear independent, which is the key property for localized multi-resolution and linear independence for non-tensor-product domain. And then, we prove that the number of $T$-spline control points which contribute each Bézier element is optimal, which is very important to obtain a bound for the number of non zero entries in the mass and stiffness matrices for IGA with $T$-splines. Moreover, it is found that the elegant labeling tool for B-splines, blossom, can also be applied for analysis-suitable $T$-splines.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1504-m4493
Journal of Computational Mathematics, Vol. 33 (2015), Iss. 4 : pp. 428–442
Published online: 2015-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: $T$-splines Linear independence iso-geometric analysis Analysis-suitable $T$-splines.