2018/12/21 by Mario Kapl, Kapl, Mario, Giancarlo Sangalli +3 · 1 citation
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1812.09088
openalex publication_date 2018/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the context of isogeometric analysis, globally C1 isogeometric spaces\nover unstructured quadrilateral meshes allow the direct solution of fourth\norder partial differential equations on complex geometries via their Galerkin\ndiscretization. The design of such smooth spaces has been intensively studied\nin the last five years, in particular for the case of planar domains, and is\nstill task of current research. In this paper, we first give a short survey of\nthe developed methods and especially focus on the approach [26]. There, the\nconstruction of a specific C1 isogeometric spline space for the class of\nso-called analysis-suitable G1 multi-patch parametrizations is presented.\nThis particular class of parameterizations comprises exactly those multi-patch\ngeometries, which ensure the design of C1 spaces with optimal approximation\nproperties, and allows the representation of complex planar multi-patch\ndomains. We present known results in a coherent framework, and also extend the\nconstruction to parametrizations that are not analysis-suitable G1 by\nallowing higher-degree splines in the neighborhood of the extraordinary\nvertices and edges. Finally, we present numerical tests that illustrate the\nbehavior of the proposed method on representative examples.\n