We investigate the application of immersed boundary approaches in isogeometric analysis for the treatment of flexible domains by suitably incorporating trimming operations and geometry mappings. The considered immersed-isogeometric model is framed in the context of an automatic adaptive scheme to solve linear elasticity problems. The proposed method leads to a symmetric system of linear equations, and it is essentially free of user-defined penalty and stabilization parameters. Adaptivity is achieved by employing hierarchically nested spline spaces. In particular, we focus on truncated hierarchical box splines (THBox-splines) defined over regular triangulations. Several numerical examples demonstrate the optimal convergence of the adaptive scheme.

Giannelli, C., Kanduc, T., Pelosi, F., Speleers, H. (2019). An immersed-isogeometric model: Application to linear elasticity and implementation with THBox-splines. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 349, 410-423 [10.1016/j.cam.2018.09.027].

An immersed-isogeometric model: Application to linear elasticity and implementation with THBox-splines

Pelosi F.;Speleers H.
2019

Abstract

We investigate the application of immersed boundary approaches in isogeometric analysis for the treatment of flexible domains by suitably incorporating trimming operations and geometry mappings. The considered immersed-isogeometric model is framed in the context of an automatic adaptive scheme to solve linear elasticity problems. The proposed method leads to a symmetric system of linear equations, and it is essentially free of user-defined penalty and stabilization parameters. Adaptivity is achieved by employing hierarchically nested spline spaces. In particular, we focus on truncated hierarchical box splines (THBox-splines) defined over regular triangulations. Several numerical examples demonstrate the optimal convergence of the adaptive scheme.
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/08 - Analisi Numerica
English
Con Impact Factor ISI
Box splines; Immersed boundary method; Isogeometric analysis; Linear elasticity; Local refinement; Truncated hierarchical splines; Weak boundary conditions
Giannelli, C., Kanduc, T., Pelosi, F., Speleers, H. (2019). An immersed-isogeometric model: Application to linear elasticity and implementation with THBox-splines. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 349, 410-423 [10.1016/j.cam.2018.09.027].
Giannelli, C; Kanduc, T; Pelosi, F; Speleers, H
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/214800
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