On the approximation power of generalized T-splines

被引：0
作者：
Bracco, Cesare [1 ]
Cho, Durkbin [2 ]
Dagnino, Catterina [3 ]
Kim, Tae-wan [4 ]
机构：
[1] U Dini Univ Florence, Dept Math & Comp Sci, Vle Morgagni 67, I-50134 Florence, Italy
[2] Dongguk Univ, Dept Math, Pil Dong 3 Ga, Seoul 100715, South Korea
[3] G Peano Univ Turin, Dept Math, V Carlo Alberto 10, I-10123 Turin, Italy
[4] Seoul Natl Univ, Dept Naval Architecture & Ocean Engn, 1 Gwanak Ro, Seoul 151744, South Korea
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2017年 / 311卷
基金：
新加坡国家研究基金会;
关键词：
T-spline; Generalized B-spline; Partition of unity; Spline approximation; Isogeometric analysis; LINEAR INDEPENDENCE;
D O I：
10.1016/j.cam.2016.07.011
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The paper presents some properties of Generalized T-splines (GT-splines), which are crucial to their actual application. In particular, we construct a dual basis for a noteworthy class of GT-splines, which allows to show that, under suitable conditions, they form a partition of unity. Moreover, we study the approximation properties of the GT-spline space by constructing a class of quasi-interpolants which belong to it and are defined by giving a dual basis. (C) 2016 Elsevier B.V. All rights reserved.
引用
收藏
页码：423 / 438
页数：16
相关论文
共 21 条
[1]   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
[2]   Generalized T-splines and VMCR T-meshes [J].
Bracco, Cesare ;
Cho, Durkbin .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2014, 280 :176-196
[3]   Trigonometric generalized T-splines [J].
Bracco, Cesare ;
Berdinsky, Dmitry ;
Cho, Durkbin ;
Oh, Min-jae ;
Kim, Tae-wan .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2014, 268 :540-556
[4]   Linear independence of the T-spline blending functions associated with some particular T-meshes [J].
Buffa, A. ;
Cho, D. ;
Sangalli, G. .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2010, 199 (23-24) :1437-1445
[5]   On a class of weak Tchebycheff systems [J].
Costantini, P ;
Lyche, T ;
Manni, C .
NUMERISCHE MATHEMATIK, 2005, 101 (02) :333-354
[6]   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
[7]  
Cottrell J.A., 2009, Isogeometric Analysis: Towards Unification of Computer Aided Design and Finite Element Analysis
[8]   IsoGeometric analysis using T-splines on two-patch geometries [J].
da Veiga, L. Beira ;
Buffa, A. ;
Cho, D. ;
Sangalli, G. .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2011, 200 (21-22) :1787-1803
[9]   Mathematical analysis of variational isogeometric methods [J].
da Veiga, L. Beirao ;
Buffa, A. ;
Sangalli, G. ;
Vazquez, R. .
ACTA NUMERICA, 2014, 23 :157-287
[10]   ANALYSIS-SUITABLE T-SPLINES OF ARBITRARY DEGREE: DEFINITION, LINEAR INDEPENDENCE AND APPROXIMATION PROPERTIES [J].
Da Veiga, L. Beirao ;
Buffa, A. ;
Sangalli, G. ;
Vazquez, R. .
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2013, 23 (11) :1979-2003
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