Volume 33, Issue 4
Some Properties for Analysis-Suitable $T$-Splines

J. Comp. Math., 33 (2015), pp. 428-442.

Published online: 2015-08

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• 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.

• Keywords

$T$-splines, Linear independence, iso-geometric analysis, Analysis-suitable $T$-splines.

65D07

lixustc@ustc.edu.cn (Xin Li)

• BibTex
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@Article{JCM-33-428, author = {Li , Xin}, title = {Some Properties for Analysis-Suitable $T$-Splines}, journal = {Journal of Computational Mathematics}, year = {2015}, volume = {33}, number = {4}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1504-m4493}, url = {http://global-sci.org/intro/article_detail/jcm/9852.html} }
TY - JOUR T1 - Some Properties for Analysis-Suitable $T$-Splines AU - Li , Xin JO - Journal of Computational Mathematics VL - 4 SP - 428 EP - 442 PY - 2015 DA - 2015/08 SN - 33 DO - http://doi.org/10.4208/jcm.1504-m4493 UR - https://global-sci.org/intro/article_detail/jcm/9852.html KW - $T$-splines, Linear independence, iso-geometric analysis, Analysis-suitable $T$-splines. AB -

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.

Xin Li. (2019). Some Properties for Analysis-Suitable $T$-Splines. Journal of Computational Mathematics. 33 (4). 428-442. doi:10.4208/jcm.1504-m4493
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