We present a framework for geometric design and isogeometric analysis on unstructured quadrilateral meshes. Acknowledging the differing requirements posed by design (e.g., the convenience of an intuitive control net) and analysis (e.g., good approximation behavior), we propose the construction of a separate, smooth spline space for each while ensuring isogeometric compatibility – requiring the geometric models to be members of the analysis-suitable spaces. The methodology is simple and is presented for bi-cubic splines; extensions to higher degrees are possible, and are briefly discussed. The presentation has been structured to show compatibility with T-splines – a state-of-the-art CAD technology – but the approach should extend to other locally refinable spline technologies (based on local tensor-product structures). An instantiation of the framework is presented, and several numerical tests focused on geometric design and isogeometric analysis demonstrate the versatility of the developed framework, and show significantly higher convergence rates than attained previously in the considered setting.

Toshniwal, D., Speleers, H., Hughes, T. (2017). Smooth cubic spline spaces on unstructured quadrilateral meshes with particular emphasis on extraordinary points: geometric design and isogeometric analysis considerations. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 327, 411-458 [10.1016/j.cma.2017.06.008].

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

Speleers H.;
2017-12-01

Abstract

We present a framework for geometric design and isogeometric analysis on unstructured quadrilateral meshes. Acknowledging the differing requirements posed by design (e.g., the convenience of an intuitive control net) and analysis (e.g., good approximation behavior), we propose the construction of a separate, smooth spline space for each while ensuring isogeometric compatibility – requiring the geometric models to be members of the analysis-suitable spaces. The methodology is simple and is presented for bi-cubic splines; extensions to higher degrees are possible, and are briefly discussed. The presentation has been structured to show compatibility with T-splines – a state-of-the-art CAD technology – but the approach should extend to other locally refinable spline technologies (based on local tensor-product structures). An instantiation of the framework is presented, and several numerical tests focused on geometric design and isogeometric analysis demonstrate the versatility of the developed framework, and show significantly higher convergence rates than attained previously in the considered setting.
1-dic-2017
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/08 - ANALISI NUMERICA
English
Con Impact Factor ISI
Smooth splines; Unstructured quadrilateral meshes; Extraordinary points; Isogeometric analysis; Geometric modeling
Toshniwal, D., Speleers, H., Hughes, T. (2017). Smooth cubic spline spaces on unstructured quadrilateral meshes with particular emphasis on extraordinary points: geometric design and isogeometric analysis considerations. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 327, 411-458 [10.1016/j.cma.2017.06.008].
Toshniwal, D; Speleers, H; Hughes, Tjr
Articolo su rivista
File in questo prodotto:
File Dimensione Formato  
Toshniwal_CMAME_2017_ep.pdf

solo utenti autorizzati

Tipologia: Versione Editoriale (PDF)
Licenza: Copyright dell'editore
Dimensione 3.19 MB
Formato Adobe PDF
3.19 MB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/215185
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 89
  • ???jsp.display-item.citation.isi??? 82
social impact