The space of C1-smooth isogeometric spline functions on trilinearly parameterized volumetric two-patch domains

Abstract

We study the C1-smooth isogeometric spline space over a specific class of unstructured hexahedral meshes, namely over the class of trilinearly parameterized volumetric two-patch domains. Recently, the structure of this space was experimentally analyzed in Birner et al. (2018) by numerically computing a basis and the dimension of this space. In this work, we develop the theoretical framework to explore the C1-smooth isogeometric space. Amongst others, we use the framework to prove the numerically obtained dimension from Birner et al. (2018) and to describe a simple explicit basis construction which consists of locally supported functions.