Il Prof. Hendrik Speleers (Leuven University) terrà una conferenza dal titolo:
"THB-splines and quasi-interpolation in hierarchical spaces"
abrstact: Quasi-interpolation is a well-known technique to construct accurate approximants to given data or functions by means of a local approach. Usually it consists in a linear combination of a given system of blending functions with suitable locally constructed coefficients. Hierarchical B-splines have been introduced by Forsey and Bartels (1988) as an accumulation of tensor-product B-splines with nested knot vectors. Their aim is to allow local refinements, which are not possible in the case of classical tensor-product splines. They are of interest in different areas ranging from approximation theory to geometric modeling and isogeometric analysis, a new paradigm for the numerical treatment of partial differential equations.In this talk we discuss an alternative basis for the hierarchical space spanned by the
hierarchical B-splines, the so-called truncated basis, which has an enhanced set of properties. It provides a convex partition of unity, consisting of functions with small support. Moreover, the truncated basis is strongly stable with respect to the number of refinement levels.We also present a general approach to construct quasi-interpolants in hierarchical spaces expressed in terms of the corresponding truncated basis. Quasi-interpolants of full approximation order and/or projections can be easily obtained. The main ingredient of the construction is the property of preservation of coefficients of the truncated basis representation. Joint work with Carlotta Giannelli, Bert Juttler, Carla Manni.