Hybrid-degree weighted T-splines and their application in isogeometric analysis

- We present hybrid-degree weighted T-splines to perform local p-refinement to T-splines.
- A limited number of new control points are introduced for the local p-refinement.
- The degree of basis functions of the refined region and transition region is elevated by one after local p-refinement.

In this paper, we introduce hybrid-degree weighted T-splines by means of local p-refinement and apply them to isogeometric analysis. Standard T-splines enable local h-refinement, however, they do not support local p-refinement. To increase the flexibility of T-splines so that local p-refinement is also available, we first define weighted B-spline curves of hybrid degree. Then we extend the idea to weighted T-spline surfaces of hybrid degree. A transition region is defined so as to stitch the locally p-refined region with the rest of the mesh. The transition region has the same basis function degree as the p-refined region, and the same surface continuity as the rest of the mesh. Finally, we compare the performance of odd-, even-, and hybrid-degree T-splines over an L-shaped domain governed by the Laplace equation and create high-genus surfaces using hybrid-degree weighted T-splines.