Weakening the tight coupling between geometry and simulation in isogeometric analysis: from sub- and super-geometric analysis to geometry-independent field approximaTion (GIFT)

This paper presents an approach to generalize the concept of isogeometric analysis by allowing different spaces for the parameterization of the computational domain and for the approximation of the solution field. The method inherits the main advantage of isogeometric analysis, ie, preserves the original exact computer-aided design geometry (for example, given by nonuniform rational B-splines), but allows pairing it with an approximation space, which is more suitable/flexible for analysis, for example, T-splines, LR-splines, (truncated) hierarchical B-splines, and PHT-splines. This generalization offers the advantage of adaptive local refinement without the need to reparameterize the domain, and therefore without weakening the link with the computer-aided design model. We demonstrate the use of the method with different choices of geometry and field spaces and show that, despite the failure of the standard patch test, the optimum convergence rate is achieved for nonnested spaces.University of Luxembourg European Research Council 279578 Luxembourg National Research Funds INTER/FWO/15/10318764 INTER/MOBILITY/14/8813215/CBM/Bordas National Nature Science Foundation of China 61772163 61472111 Zhejiang Provincial Natural Science Foundation of China LR16F020003 LQ16F020005 Open Project Program of the State Key Lab of CADCG A170