Isogeometric methods for high order problems with $C^1$ hierarchical spline spaces on multipatch geometries
Please login to view abstract download link
In recent years, the combination of isogeometric analysis and spline spaces allowing local refinement led to a great development of adaptive methods for the solution of PDEs. The attempt to apply this approach to high-order problems on complex domains sparked the interest in $C^1$-smooth spaces defined on multipatch domains. Here we present a construction for $C^1$ hierarchical splines defined on multipatch domains (including non-planar ones), based on the results obtained in [1] and [3]. Specific refinement and coarsening algorithms are needed in order to guarantee that the construction always produces sets of linear independent functions. We show with a selection of numerical examples how this kind of space can be effectively employed to define adaptive isogeometric methods to solve different high-order problems (see, e.g., [2]). Bibliography [1] C. Bracco, C. Giannelli, M. Kapl, and R. V\'azquez, Adaptive isogeometric methods with C1 (truncated) hierarchical splines on planar multi-patch domains. Math. Models Methods Appl. Sci., Vol. 33, pp. 1829-1874, 2023. [2] C. Bracco, C. Giannelli, A. Reali, M. Torre and R. Vàzquez, Adaptive isogeometric phase-field modeling of the Cahn–Hilliard equation: Suitably graded hierarchical refinement and coarsening on multi-patch geometries, Comput. Methods Appl. Mech. Engrg., Vol. 417, 2023. [3] A. Farahat, B. Juettler, M. Kapl, and T. Takacs, Isogeometric analysis with $C^1$-smooth functions over multi-patch surfaces. Math. Models Methods Appl. Sci., Vol. 403, 2023.
