Construction of approximate C1 bases on two-patch domains in isogeometric analysis
Prof. Pascal Weinmüller, JKU, Linz.
Sala conferenze IMATI-CNR, Pavia – Martedì 7 Maggio 2019 h.15:00
Abstract. One key element of isogeometric analysis is that it allows high order smoothness within one patch. However, this is not the case on so-called multi-patch geometries where the global continuity is C0. Therefore, for C1 isogeometric functions, a special construction for the basis is needed. Such spaces are of interest when solving numerically fourth-order PDE problems, such as the biharmonic equation, using an isogeometric Galerkin method.
With the construction of so called analysis-suitable G1 (in short, AS-G1) parameterizations it is possible, under certain additional assumptions, to have C1 isogeometric spaces with optimal approximation properties. These geometries satisfy certain constraints along the interfaces.
The problem is that most complex geometries are not AS-G1 geometries. Therefore we define basis functions for isogeometric spaces by enforcing approximate C1 conditions. For this reason the defined function spaces are not exactly C1 but only approximately. We study the convergence behaviour and define function spaces that behave optimally under h-refinement, by locally introducing functions of higher polynomial degree and/or lower regularity. For the numerical tests we focus on the influence of a single, non-trivial interface within a two-patch domain.