### SOME PROPERTIES FOR ANALYSIS-SUITABLE T-SPLINES

Xin Li

1. School of Mathematical Science, University of Science and Technology of China, Hefei, Anhui, China
• Received:2014-02-18 Revised:2015-04-08 Online:2015-07-15 Published:2015-07-15
• Supported by:

This work was supported by the Chinese Universities Scientific Fund, the NSF of China (No.11031007, No.60903148), SRF for ROCS SE, and the CAS Startup Scientific Research Foundation and NBRPC 2011CB302400.

Xin Li. SOME PROPERTIES FOR ANALYSIS-SUITABLE T-SPLINES[J]. Journal of Computational Mathematics, 2015, 33(4): 428-442.

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-tensorproduct domain. And then, we prove that the number of T-spline control points 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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