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

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 splines 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.