Abstract
In this paper we propose a local projector for truncated hierarchical B-splines (THB-splines). The local THB-spline projector is an adaptation of the Bézier projector proposed by Thomas et al. (Comput Methods Appl Mech Eng 284, 2015) for B-splines and analysis-suitable T-splines (AS T-splines). For THB-splines, there are elements on which the restrictions of THB-splines are linearly dependent, contrary to B-splines and AS T-splines. Therefore, we cluster certain local mesh elements together such that the THB-splines with support over these clusters are linearly independent, and the Bézier projector is adapted to use these clusters. We introduce general extensions for which optimal convergence is shown theoretically and numerically. In addition, a simple adaptive refinement scheme is introduced and compared to Giust et al. (Comput. Aided Geom. Des. 80, 2020), where we find that our simple approach shows promise.
| Original language | English |
|---|---|
| Title of host publication | Springer INdAM Series |
| Publisher | Springer |
| Pages | 115-148 |
| Number of pages | 34 |
| ISBN (Print) | 978-981-97-6508-9 |
| DOIs | |
| Publication status | Published - 2024 |
Publication series
| Name | Springer INdAM Series |
|---|---|
| Volume | 60 |
| ISSN (Print) | 2281-518X |
| ISSN (Electronic) | 2281-5198 |
Bibliographical note
Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-careOtherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.