Topologically Unrestricted Isogeometric Splines on Multi-Patch Domains with Extraordinary Vertices
Philipp Langgruber  1@  
1 : JKU - Linz

Isogeometric splines on multipatch domains are needed for the discretization of partial differential
equations on general domains. However, achieving smoothness at extraordinary vertices (EVs) – while main-
taining the approximation power – is a challenging problem. Several approaches for solving this problem have
been explored in the rich literature on this topic. These may be classified into methods that (a) use the classical
notion of geometric continuity between surface patches, (b) employ singularly parameterized surfaces, (c) rely on subdivision surfaces and (d) are based on the concept of manifolds from
differential geometry. Our work aims at applications in isogeometric analysis, where it is essential to
use discretization spaces spanned by relatively simple basis functions (suitable for efficient matrix assembly via
numerical integration), which also possess good approximation power, ideally guaranteed by theoretical results.
We focus on a construction of Prautzsch, which is based on composing polynomial mappings with spline
parameterizations. We show how to generate suitable basis functions in the vicinity of EVs and discuss the
approximation power of the resulting spline space.

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