Recent developments for isogeometric methods with hierarchical B-splines
Rafael Vazquez, EPFL, Lausanne, Svizzera.
Sala conferenze IMATI-CNR, Pavia – Martedì 12 Febbraio 2019 h.16:30
Abstract. Hierarchical B-splines are probably the most successful choice for the development of adaptive isogeometric methods. The local refinement capability is obtained by a simple multilevel construction, where the set of active functions is decidded through a check on their support. They possess a sound mathematical theory for adaptive refinement, which is based on admissible meshes, a class of suitably graded meshes.
In this talk I will present several recent results towards the efficient use of hierarchical B-splines. I will first present a coarsening algorithm for the construction of admissible mehes, and show its advantages in the solution of the transient heat equation with a moving heat source. I will also present the construction of an additive multilevel preconditioner, based on admissible meshes, in such a way that the condition number is bounded and independent of the number of levels. In the last part of the talk I will show results on the construction of hierarchical C^1 basis functions on geometries constructed with two patches.