Close Search Advanced
Journals
Resources
About Us
Open Access

Some Properties for Analysis-Suitable $T$-Splines

Some Properties for Analysis-Suitable $T$-Splines
Preview
Add to basket

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.

Submit Article

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

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.

Author Details

Xin Li

  1. Quasi-interpolation for analysis-suitable T-splines

    Kang, Hongmei | Yong, Zhiguo | Li, Xin

    Computer Aided Geometric Design, Vol. 98 (2022), Iss. P.102147

    https://doi.org/10.1016/j.cagd.2022.102147 [Citations: 1]

  2. Topology optimization with precise evolving boundaries based on IGA and untrimming techniques

    Shakour, Emad | Amir, Oded

    Computer Methods in Applied Mechanics and Engineering, Vol. 374 (2021), Iss. P.113564

    https://doi.org/10.1016/j.cma.2020.113564 [Citations: 13]

  3. An unsteady 3D Isogeometrical Boundary Element Analysis applied to nonlinear gravity waves

    Maestre, Jorge | Cuesta, Ildefonso | Pallares, Jordi

    Computer Methods in Applied Mechanics and Engineering, Vol. 310 (2016), Iss. P.112

    https://doi.org/10.1016/j.cma.2016.06.031 [Citations: 10]

  4. An isogeometric finite element formulation for phase transitions on deforming surfaces

    Zimmermann, Christopher | Toshniwal, Deepesh | Landis, Chad M. | Hughes, Thomas J.R. | Mandadapu, Kranthi K. | Sauer, Roger A.

    Computer Methods in Applied Mechanics and Engineering, Vol. 351 (2019), Iss. P.441

    https://doi.org/10.1016/j.cma.2019.03.022 [Citations: 30]

  5. Improved local refinement for S-splines-based isogeometric analysis

    Hu, Wenkai | Li, Xin | Shen, Li-Yong | Sederberg, T.W.

    Computer Methods in Applied Mechanics and Engineering, Vol. 416 (2023), Iss. P.116337

    https://doi.org/10.1016/j.cma.2023.116337 [Citations: 0]

  6. Adaptive refinement for unstructured T-splines with linear complexity

    Maier, Roland | Morgenstern, Philipp | Takacs, Thomas

    Computer Aided Geometric Design, Vol. 96 (2022), Iss. P.102117

    https://doi.org/10.1016/j.cagd.2022.102117 [Citations: 1]

  7. Mathematical Foundations of Adaptive Isogeometric Analysis

    Buffa, Annalisa | Gantner, Gregor | Giannelli, Carlotta | Praetorius, Dirk | Vázquez, Rafael

    Archives of Computational Methods in Engineering, Vol. 29 (2022), Iss. 7 P.4479

    https://doi.org/10.1007/s11831-022-09752-5 [Citations: 16]

  8. Smooth cubic spline spaces on unstructured quadrilateral meshes with particular emphasis on extraordinary points: Geometric design and isogeometric analysis considerations

    Toshniwal, Deepesh | Speleers, Hendrik | Hughes, Thomas J.R.

    Computer Methods in Applied Mechanics and Engineering, Vol. 327 (2017), Iss. P.411

    https://doi.org/10.1016/j.cma.2017.06.008 [Citations: 105]

  9. Seamless integration of design and Kirchhoff–Love shell analysis using analysis-suitable unstructured T-splines

    Casquero, Hugo | Wei, Xiaodong | Toshniwal, Deepesh | Li, Angran | Hughes, Thomas J.R. | Kiendl, Josef | Zhang, Yongjie Jessica

    Computer Methods in Applied Mechanics and Engineering, Vol. 360 (2020), Iss. P.112765

    https://doi.org/10.1016/j.cma.2019.112765 [Citations: 74]

  10. Local Mesh Refinement and Coarsening Based on Analysis-Suitable T-Splines Surface and Its Application in Contact Problem

    Wang, Yue | Yu, Zuqing | Lan, Peng | Lu, Nianli

    Journal of Computational and Nonlinear Dynamics, Vol. 17 (2022), Iss. 10

    https://doi.org/10.1115/1.4055142 [Citations: 3]

  11. Hybrid-degree weighted T-splines and their application in isogeometric analysis

    Liu, Lei | Casquero, Hugo | Gomez, Hector | Zhang, Yongjie Jessica

    Computers & Fluids, Vol. 141 (2016), Iss. P.42

    https://doi.org/10.1016/j.compfluid.2016.03.020 [Citations: 8]

  12. de Boor-like evaluation algorithm for Analysis-suitable T-splines

    Kang, Hongmei | Li, Xin

    Graphical Models, Vol. 106 (2019), Iss. P.101042

    https://doi.org/10.1016/j.gmod.2019.101042 [Citations: 3]