We describe a construction of locally supported spline projectors for truncated hierarchical (TH) B-splines.
These operators, which are based on restricted hierarchical spline fitting, can be used to generate approximations
of functions in adaptively refined spline spaces [1]. We discuss the computational efficiency of the resulting
algorithms. In addition, we show that these projectors can be employed successfully for the discretization
of partial differential equations via isogeometric collocation. More precisely, we combine the framework of
weighted isogeometric collocation [2] with the THB-spline projectors and discuss the computational efficiency
of the algorithms and the convergence properties of the resulting discretization scheme [3].

Joint work with Alessandro Giust.

References:

[1] A. Giust, B. Jüttler and A. Mantzaflaris. Local (T)HB-spline projectors via restricted hierarchical spline
fitting, Computer Aided Geometric Design, 80, article no. 101865, 2020.
[2] D. Schillinger, J. Evans, A. Reali, M. Scott and T. Hughes. Isogeometric collocation: Cost comparison
with Galerkin methods and extension to adaptive hierarchical NURBS discretizations. Computer Methods
in Applied Mechanics and Engineering, 267, pages 170–232, 2013.
[3] A. Giust and B. Jüttler. Weighted isogeometric collocation based on spline projectors, Computer Methods
in Applied Mechanics and Engineering, 391, article no. 114554, 2022.