Space of [formula omitted]-smooth geometrically continuous isogeometric functions on planar multi-patch geometries: Dimension and numerical experiments

Abstract

We study the space of C2-smooth isogeometric functions on bilinearly parameterized multi-patch domains Ω⊂R2, where the graph of each isogeometric function is a multi-patch spline surface of bidegree (d,d), d∈{5,6}. The space is fully characterized by the equivalence of the C2-smoothness of an isogeometric function and the G2-smoothness of its graph surface (cf. Groisser and Peters (2015), Kapl et al. (2015)). This is the reason to call its functions C2-smooth geometrically continuous isogeometric functions.In particular, the dimension of this C2-smooth isogeometric space is investigated. The study is based on the decomposition of the space into three subspaces and is an extension of the work Kapl and Vitrih (2017) to the multi-patch case. In addition, we present an algorithm for the construction of a basis, and use the resulting globally C2-smooth functions for numerical experiments, such as performing L2 approximation and solving triharmonic equation, on bilinear multi-patch domains. The numerical results indicate optimal approximation order.