2020/08/14 by Mario Kapl, Kapl, Mario, Vito Vitrih +1 · 1 citation
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #FOS: Mathematics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2008.06247
openalex publication_date 2020/08/14 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
The design of globally Cs-smooth (s \≥ 1) isogeometric spline spaces\nover multi-patch geometries is a current and challenging topic of research in\nthe framework of isogeometric analysis. In this work, we extend the recent\nmethods [25,28] and [31-33] for the construction of C1-smooth and\nC2-smooth isogeometric spline spaces over particular planar multi-patch\ngeometries to the case of Cs-smooth isogeometric multi-patch spline spaces\nof an arbitrary selected smoothness s \≥ 1. More precisely, for any s \≥\n1, we study the space of Cs-smooth isogeometric spline functions defined on\nplanar, bilinearly parameterized multi-patch domains, and generate a particular\nCs-smooth subspace of the entire Cs-smooth isogeometric multi-patch\nspline space. We further present the construction of a basis for this\nCs-smooth subspace, which consists of simple and locally supported\nfunctions. Moreover, we use the Cs-smooth spline functions to perform L2\napproximation on bilinearly parameterized multi-patch domains, where the\nobtained numerical results indicate an optimal approximation power of the\nconstructed Cs-smooth subspace.\n