Geodesic
Local and Adaptive Refinement with Hierarchical B-splines
Bollettino della Unione matematica italiana, Série 9, Tome 6 (2013) no. 3, pp. 735-740.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

Adaptive spline models for geometric modeling and spline-based PDEs solvers have recently attracted increasing attention both in the context of computer aided geometric design and isogeometric analysis. In particular, approximation spaces defined over extensions of tensor-product meshes which allow axis aligned segments with T-junctions are currently receiving particular attention. In this short paper we review some recent results concerning the characterization of the space spanned by the hierarchical B-spline basis. In addition, we formulate a refinement algorithm which allows us to satisfy the conditions needed for this characterization. 
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Giannelli, Carlotta; Jüttler, Bert. Local and Adaptive Refinement with Hierarchical B-splines. Bollettino della Unione matematica italiana, Série 9, Tome 6 (2013) no. 3, pp. 735-740. http://geodesic.mathdoc.fr/item/BUMI_2013_9_6_3_a15/

[1] A. Buffa, D. Cho and G. Sangalli, Linear independence of the T-spline blending functions associated with some particular T-meshes, Comput. Methods Appl. Mech. Engrg., 199 (2010), 1437-1445. | DOI | MR | Zbl

[2] M.R. Dörfel, B. Jüttler and B. Simeon, Adaptive Isogeometric Analysis by Local h-Refinement with T-splines, Comput. Methods Appl. Mech. Engrg., 199 (2010), 264-275. | DOI | MR

[3] D.R. Forsey and R.H. Bartels, Hierarchical B-spline refinement, Comput. Graphics, 22 (1988), 205-212.

[4] D.R. Forsey and R.H. Bartels, Surface fitting with hierarchical splines, ACM Trans. Graphics, 14 (1995), 134-161.

[5] C. Giannelli, B. Jüttler and H. Speleers, THB-splines: the truncated basis for hierarchical splines. Comput. Aided Geom. Design, 29 (2012), 485-498. | DOI | MR | Zbl

[6] C. Giannelli, B. Jüttler and H. Speleers, Strongly stable bases for adaptively refined multilevel spline spaces, Adv. Comp. Math., to appear (2013). | DOI | MR

[7] C. Giannelli and B. Jüttler, Bases and dimensions of bivariate hierarchical tensor-product splines, J. Comput. Appl. Math., 239 (2013), 162-178. | DOI | MR | Zbl

[8] T.J.R. Hughes, J.A. Cottrell and Y. Bazilevs, Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Comput. Methods Appl. Mech. Engrg., 194 (2005), 4135-4195. | DOI | MR | Zbl

[9] R. Kraft, Adaptive and linearly independent multilevel B-splines, in: LE MÉHAUTÉ A., RABUT C. and SCHUMAKER L.L. (Eds.), Surface Fitting and Multiresolution Methods, Vanderbilt University Press, Nashville (1997), 209-218. | MR | Zbl

[10] R. Kraft, Adaptive und linear unabhängige Multilevel B-Splines und ihre Anwendungen, PhD Thesis, Universität Stuttgart (1998). | MR | Zbl

[11] A.-V. Vuong, C. Giannelli, B. Jüttler and B. Simeon, A hierarchical approach to adaptive local refinement in isogeometric analysis, Comput. Methods Appl. Mech. Engrg., 200 (2011), 3554-3567. | DOI | MR | Zbl