2019/01/28 by Cesare Bracco, Carlotta Giannelli, Bracco, Cesare +5
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #FOS: Mathematics #Numerical Analysis (math.NA) #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1901.09689
openalex publication_date 2019/01/28 · openalex created_date 2022/07/30 · openalex updated_date 2026/07/28
Adaptive isogeometric methods for the solution of partial differential\nequations rely on the construction of locally refinable spline spaces. A simple\nand efficient way to obtain these spaces is to apply the multi-level\nconstruction of hierarchical splines, that can be used on single-patch domains\nor in multi-patch domains with C0 continuity across the patch interfaces.\nDue to the benefits of higher continuity in isogeometric methods, recent works\ninvestigated the construction of spline spaces with global C1 continuity on\ntwo or more patches. In this paper, we show how these approaches can be\ncombined with the hierarchical construction to obtain global C1 continuous\nhierarchical splines on two-patch domains. A selection of numerical examples is\npresented to highlight the features and effectivity of the construction.\n