Isogeometric analysis with C1 hierarchical functions on planar two-patch geometries. (1st December 2020)

• Record Type: Journal Article
• Authors: Bracco, Cesare; Giannelli, Carlotta; Kapl, Mario; Vázquez, Rafael
• Is Part Of: Computers & mathematics with applications. Volume 80:issue 11(2020)
• Page Start: 2538
• Page End: 2562
• Publication Date: 2020-12-01
• Subjects: Isogeometric analysis -- Geometric continuity -- Two-patch domain -- Hierarchical splines -- Local refinement; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2020.03.018
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: Adaptive isogeometric methods for the solution of partial differential equations rely on the construction of locally refinable spline spaces. A simple and efficient way to obtain these spaces is to apply the multi-level construction of hierarchical splines, that can be used on single-patch domains or in multi-patch domains with C 0 continuity across the patch interfaces. Due to the benefits of higher continuity in isogeometric methods, recent works investigated the construction of spline spaces with global C 1 continuity on two or more patches. In this paper, we show how these approaches can be combined with the hierarchical construction to obtain global C 1 continuous hierarchical splines on two-patch domains. A selection of numerical examples is presented to highlight the features and effectivity of the construction.