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.
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
Center for Computational Mathematics9500 Gilman Dr. #0112La Jolla, CA 92093-0112Tel: (858)534-9813