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Axioms 2018, 7(3), 43; https://doi.org/10.3390/axioms7030043

Refinement Algorithms for Adaptive Isogeometric Methods with Hierarchical Splines

1
Dipartimento di Matematica e Informatica “U. Dini”, Università degli Studi di Firenze, Viale Morgagni 67/A, 50134 Florence, Italy
2
Institute of Mathematics, Ecole Polytechnique Fédérale de Lausanne, Station 8, 1015 Lausanne, Switzerland
3
Istituto di Matematica Applicata e Tecnologie Informatiche “E. Magenes” del CNR, via Ferrata 5, 27100 Pavia, Italy
*
Author to whom correspondence should be addressed.
Received: 11 May 2018 / Revised: 16 June 2018 / Accepted: 18 June 2018 / Published: 21 June 2018
(This article belongs to the Special Issue Advanced Numerical Methods in Applied Sciences)
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Abstract

The construction of suitable mesh configurations for spline models that provide local refinement capabilities is one of the fundamental components for the analysis and development of adaptive isogeometric methods. We investigate the design and implementation of refinement algorithms for hierarchical B-spline spaces that enable the construction of locally graded meshes. The refinement rules properly control the interaction of basis functions at different refinement levels. This guarantees a bounded number of nonvanishing (truncated) hierarchical B-splines on any mesh element. The performances of the algorithms are validated with standard benchmark problems. View Full-Text
Keywords: isogeometric analysis; adaptive methods; hierarchical splines; THB-splines; local refinement isogeometric analysis; adaptive methods; hierarchical splines; THB-splines; local refinement
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Bracco, C.; Giannelli, C.; Vázquez, R. Refinement Algorithms for Adaptive Isogeometric Methods with Hierarchical Splines. Axioms 2018, 7, 43.

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