13.04.2018 | 11:00 bis 12:00

Seminar in Numerical Analysis: Philipp Morgenstern

Philipp Morgenstern (Leibniz Universität Hannover)

Mesh Refinement for T-splines in any dimension

We introduce a mesh refinement algorithm for the Adaptive Isogeometric
Method using multivariate T-splines. We investigate linear independence
of the T-splines, nestedness of the T-spline spaces, and linear
complexity in the sense of a uniform upper bound on the ratio of
generated and marked elements, which is crucial for a later proof of
rate-optimality of the method. Altogether, this work paves the way for a
provably rate-optimal Adaptive Isogeometric Method with T-splines in any
space dimension.

As an outlook to future work, we outline an approach for the handling of
zero knot intervals and multiple lines in the interior of the domain,
which are used in CAD applications for controlling the continuity of the
spline functions, and we also sketch basic ideas for the local
refinement of two-dimensional meshes that do not have tensor-product




For further information about the seminar, please visit this webpage.