Quasi-interpolation for analysis-suitable T-splines

被引：5
作者：
Kang, Hongmei [1 ]
Yong, Zhiguo [1 ]
Li, Xin [2 ]
机构：
[1] Soochow Univ, Sch Math Sci, 1 Shizi Rd, Suzhou 215006, Jiangsu, Peoples R China
[2] Univ Sci & Technol China, Sch Math Sci, 96 Jinzhai Rd, Hefei 230026, Anhui, Peoples R China
来源：
COMPUTER AIDED GEOMETRIC DESIGN | 2022年 / 98卷
基金：
中国国家自然科学基金;
关键词：
Quasi-interpolation; Quasi-interpolants; Marsden?s identity; Analysis-suitable T-splines; SURFACE RECONSTRUCTION; ISOGEOMETRIC ANALYSIS; LINEAR INDEPENDENCE; POLYNOMIAL SPLINES; LOCAL REFINEMENT; NURBS;
D O I：
10.1016/j.cagd.2022.102147
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
We propose a novel local approximation method for analysis-suitable T-spline (AS T-spline) spaces via quasi-interpolation. The quasi-interpolants are defined as linear combination of the approximated function's values at appropriately chosen points. Benefited from the inherent nice properties of AS T-splines, the proposed quasi-interpolants can reproduce polynomials up to the same degree of AS T-spline spaces and can provide optimal approximation order. Some numerical examples of specific quasi-interpolants for bi-cubic AS T-splines are investigated to show the stability and efficiency. (C) 2022 Elsevier B.V. All rights reserved.
引用
收藏
页数：12
相关论文
共 50 条
[21]   Quasi-interpolation projectors for box splines [J].
Lyche, Tom ;
Manni, Carla ;
Sablonniere, Paul .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2008, 221 (02) :416-429
[22]   Quasi-interpolation in isogeometric analysis based on generalized B-splines [J].
Costantini, Paolo ;
Manni, Carla ;
Pelosi, Francesca ;
Sampoli, M. Lucia .
COMPUTER AIDED GEOMETRIC DESIGN, 2010, 27 (08) :656-668
[23]   Quasi-interpolation by splines on the uniform knot sets [J].
Leetma, E. ;
Vainikko, G. .
MATHEMATICAL MODELLING AND ANALYSIS, 2007, 12 (01) :107-120
[24]   Truncated T-splines: Fundamentals and methods [J].
Wei, Xiaodong ;
Zhang, Yongjie ;
Liu, Lei ;
Hughes, Thomas J. R. .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2017, 316 :349-372
[25]   de Boor-suitable (DS) T-splines [J].
Zhang, Yang ;
Pataranutaporn, Visit ;
Goldman, Ron .
GRAPHICAL MODELS, 2018, 97 :40-49
[26]   Adaptive refinement of hierarchical T-splines [J].
Chen, L. ;
de Borst, R. .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2018, 337 :220-245
[27]   GLOBALLY STRUCTURED THREE-DIMENSIONAL ANALYSIS-SUITABLE T-SPLINES: DEFINITION, LINEAR INDEPENDENCE AND m-GRADED LOCAL REFINEMENT [J].
Morgenstern, Philipp .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2016, 54 (04) :2163-2186
[28]   Locally Refined T-splines [J].
Chen, L. ;
de Borst, R. .
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2018, 114 (06) :637-659
[29]   QUASI-INTERPOLATION BY THIN-PLATE SPLINES ON A SQUARE [J].
BEATSON, RK ;
LIGHT, WA .
CONSTRUCTIVE APPROXIMATION, 1993, 9 (04) :407-433
[30]   Isogeometric analysis using T-splines [J].
Bazilevs, Y. ;
Calo, V. M. ;
Cottrell, J. A. ;
Evans, J. A. ;
Hughes, T. J. R. ;
Lipton, S. ;
Scott, M. A. ;
Sederberg, T. W. .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2010, 199 (5-8) :229-263
12345