Local and Adaptive Refinement with Hierarchical B-splines

Carlotta Giannelli; Bert Jüttler

Bollettino dell'Unione Matematica Italiana (2013)

  • Volume: 6, Issue: 3, page 735-740
  • ISSN: 0392-4041

Abstract

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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.

How to cite

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Giannelli, Carlotta, and Jüttler, Bert. "Local and Adaptive Refinement with Hierarchical B-splines." Bollettino dell'Unione Matematica Italiana 6.3 (2013): 735-740. <http://eudml.org/doc/294045>.

@article{Giannelli2013,
abstract = {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.},
author = {Giannelli, Carlotta, Jüttler, Bert},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {735-740},
publisher = {Unione Matematica Italiana},
title = {Local and Adaptive Refinement with Hierarchical B-splines},
url = {http://eudml.org/doc/294045},
volume = {6},
year = {2013},
}

TY - JOUR
AU - Giannelli, Carlotta
AU - Jüttler, Bert
TI - Local and Adaptive Refinement with Hierarchical B-splines
JO - Bollettino dell'Unione Matematica Italiana
DA - 2013/10//
PB - Unione Matematica Italiana
VL - 6
IS - 3
SP - 735
EP - 740
AB - 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.
LA - eng
UR - http://eudml.org/doc/294045
ER -

References

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  9. KRAFT, R., 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. Zbl0937.65014MR1659975
  10. KRAFT, R., Adaptive und linear unabhängige Multilevel B-Splines und ihre Anwendungen, PhD Thesis, Universität Stuttgart (1998). Zbl0903.68195MR1641654
  11. VUONG, A.-V., GIANNELLI, C., JÜTTLER, B. and SIMEON, B., A hierarchical approach to adaptive local refinement in isogeometric analysis, Comput. Methods Appl. Mech. Engrg., 200 (2011), 3554-3567. Zbl1239.65013MR2851579DOI10.1016/j.cma.2011.09.004

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