Isogeometric analysis is a recently developed framework based on finite element analysis, where the simple building blocks in geometry and solution space are replaced by more complex and geometrically-oriented compounds. Box splines are an established tool to model complex geometry, and form an intermediate approach between classical tensor-product B-splines and splines over triangulations. Local refinement can be achieved by considering hierarchically nested sequences of box spline spaces. Since box splines do not offer special elements to impose boundary conditions for the numerical solution of partial differential equations (PDEs), we discuss a weak treatment of such boundary conditions. Along the domain boundary, an appropriate domain strip is introduced to enforce the boundary conditions in a weak sense. The thickness of the strip is adaptively defined in order to avoid unnecessary computations. Numerical examples show the optimal convergence rate of box splines and their hierarchical variants for the solution of PDEs.

Kanduc, T., Giannelli, C., Pelosi, F., Speleers, H. (2017). Adaptive isogeometric analysis with hierarchical box splines. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 316, 817-838 [10.1016/j.cma.2016.09.046].

Adaptive isogeometric analysis with hierarchical box splines

Pelosi F.;Speleers H.
2017-01-01

Abstract

Isogeometric analysis is a recently developed framework based on finite element analysis, where the simple building blocks in geometry and solution space are replaced by more complex and geometrically-oriented compounds. Box splines are an established tool to model complex geometry, and form an intermediate approach between classical tensor-product B-splines and splines over triangulations. Local refinement can be achieved by considering hierarchically nested sequences of box spline spaces. Since box splines do not offer special elements to impose boundary conditions for the numerical solution of partial differential equations (PDEs), we discuss a weak treatment of such boundary conditions. Along the domain boundary, an appropriate domain strip is introduced to enforce the boundary conditions in a weak sense. The thickness of the strip is adaptively defined in order to avoid unnecessary computations. Numerical examples show the optimal convergence rate of box splines and their hierarchical variants for the solution of PDEs.
2017
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/08 - ANALISI NUMERICA
English
Adaptivity; Hierarchical box splines; Isogeometric analysis; Local refinement; Truncated hierarchical box splines; Weak boundary conditions
Kanduc, T., Giannelli, C., Pelosi, F., Speleers, H. (2017). Adaptive isogeometric analysis with hierarchical box splines. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 316, 817-838 [10.1016/j.cma.2016.09.046].
Kanduc, T; Giannelli, C; Pelosi, F; Speleers, H
Articolo su rivista
File in questo prodotto:
File Dimensione Formato  
Kanduc_CMAME_2017_box.pdf

solo utenti autorizzati

Tipologia: Versione Editoriale (PDF)
Licenza: Copyright dell'editore
Dimensione 3.08 MB
Formato Adobe PDF
3.08 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/2108/214798
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 23
  • ???jsp.display-item.citation.isi??? 21
social impact