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Truncated Hierarchical B-Splines; Hierarchies Generated by Nested Generating Systems

Bert Juettler and Urska Zore
Johannes Kepler University, Linz, Austria


Part1: The interest in hierarchical techniques for tensor-product splines has increased recently due to the need for adaptive refinement in numerical simulation via isogeometric analy- sis. The newly introduced truncated hierarchical B-spline (THB) basis of hierarchical splines possesses several ad- vantageous properties, such as partition of unity, increased sparsity and improved stability. The talk will report recent results concerning completeness, stability, approximation power and implementation aspects of THB splines. Part 2: In order to provide the possibility of local refinement, sev- eral generalizations of tensor-product splines have been ex- plored, such as hierarchical splines. We consider a gener- alized hierarchical spline space which is based on a nested sequence of (possibly linearly dependent) generating sys- tems, such as box-splines. We analyze the properties of the space obtained by collecting functions with respect to a decreasing sequence of hierarchical domains and explore applications in geometric design. Bio: Bert Juettler obtained his PhD in 1994 from Darmstadt University of technology, Germany. Since 2000 he is professor of scientific computing at Johannes Kepler University, Linz, Austria. His research interests include geometric design and computing and isogeometric analysis. Urska Zore obtained her Master degree in Mathematics from the University of Ljubljana, Slovenija, in 2012. Since January 2013 she is a PhD candidate at Johannes Kepler University, Linz, Austria.

Friday, November 15, 2013
1:00PM AP&M 2402