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

Abstract 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.

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