2020/08/14 by Mario Kapl, Kapl, Mario, Vito Vitrih +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #FOS: Mathematics #Numerical Analysis (math.NA) #cs.NA #math.NA
paper · pdf · doi:10.48550/arxiv.2008.06247
arxiv created 2020/08/14 · openalex publication_date 2020/08/14 · arxiv updated 2020/08/17 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
The design of globally Cs-smooth (s ≥ 1) isogeometric spline spaces over multi-patch geometries is a current and challenging topic of research in the framework of isogeometric analysis. In this work, we extend the recent methods [25,28] and [31-33] for the construction of C1-smooth and C2-smooth isogeometric spline spaces over particular planar multi-patch geometries to the case of Cs-smooth isogeometric multi-patch spline spaces of an arbitrary selected smoothness s ≥ 1. More precisely, for any s ≥ 1, we study the space of Cs-smooth isogeometric spline functions defined on planar, bilinearly parameterized multi-patch domains, and generate a particular Cs-smooth subspace of the entire Cs-smooth isogeometric multi-patch spline space. We further present the construction of a basis for this Cs-smooth subspace, which consists of simple and locally supported functions. Moreover, we use the Cs-smooth spline functions to perform L2 approximation on bilinearly parameterized multi-patch domains, where the obtained numerical results indicate an optimal approximation power of the constructed Cs-smooth subspace.