Prof. Dr. Bert Jüttler, Johannes Kepler Universität Linz

Isogeometric Analysis is a computational framework for numerical simulation, which was introduced by T.J.R. Hughes et al. in 2005 with the aim of bridging the gap between Design and Analysis, by adopting the prevailing mathematical technology of tensor product splines for discretizing of partial differential equations (PDEs). This presentation will address two of the many challenges that arise in this context.
First, while the use of spline discretizations clearly offers advantages in terms of the number of degrees of freedom required compared to classical finite elements, these advantages are then compromised by the higher computational cost of matrix assembly in isogeometric analysis. We describe our methods for efficient matrix assembly, which make use of spline projection, pre-computed look-up tables and sum factorization to optimize the computational performance of the entire process.
Second, since the rigid structure of tensor product splines is an obstacle to the use of adaptive refinement in isogeometric analysis, various generalizations of them have been proposed in the literature. These include T-splines (introduced by Sederberg et al. In 2003), hierarchical B-splines (invented by Forsey and Bartels in 1988) and the so-called "locally refined" splines (Dokken et al. 2013). In this presentation, we will analyze these approaches and compare them with the truncated variant of hierarchical B-splines, which reconciles the requirements of isogeometric analysis with those of geometric design.