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.
2019-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.