Tuesday, 12 February 2019, 4.30 p.m. (sharp),

Dr. Rafael Vazquez, EPFL, Losanna, Svizzera

at the conference room of IMATI-CNR in Pavia, will give a lecture titled:

Quadrature schemes for isogeometric boundary element method with hierarchical B-splines

as part of the Applied Mathematics Seminar (IMATI-CNR e Dipartimento di Matematica, Pavia).

At the end a refreshment will be organized.

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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 decided 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 meshes, 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.