Planar domain parameterization with THB-splines

Isogeometric analysis uses spline parameterizations to describe the geometry of the physical domain. If such a parameterization is not available, it has to be generated from the domain boundaries. The construction of a good parameterization is crucial since it strongly influences the accuracy of the subsequent analysis. It is of interest to use adaptive techniques such as hierarchical splines for the parameterization, since this facilitates an accurate representation of detailed geometries and potentially improves the efficiency of the subsequent numerical simulation. We use truncated hierarchical (TH) B-splines to generate hierarchical spline spaces, since these functions possess many useful properties, such as linear independence and the fact that they form a non-negative partition of unity. In order to address the trade-off between computational effort and level of difficulty of a specific instance of the problem, we propose three levels of domain parameterization techniques that are based on THB-splines.