PARADISE · Parameterization of computational domains for isogeometric analysis

Parameterization of computational domains for isogeometric analysis

The PARADISE project was devoted to the study of innovative paradigms for geometric design and numerical simulations connected with the emerging research field of isogeometric analysis (IA), a modern paradigm for the numerical solution of partial differential equations which uses the same representation model for the simulation phase. The isogeometric methodology promotes a better integration of the numerical solver with the computer aided design (CAD) system by also simplifying the mesh refinement procedure. By considering the same smooth function spaces from the design environment to the analytical context, the isogeometric approach will potentially lead to major improvements of the product design process in certain parts of industrial applications. The use of isogeometric solvers in several application scenarios has already shown the potential of this analysis framework with respect to improvements in the convergence and smoothness properties of the numerical solution. At the same time, the development of these models leads to new challenging problems for geometric design, which are related to the representation of computational domains by parameterisations based on suitable spline techniques. One key point of interest is the construction of locally refinable spaces of test functions for IA, as possible extensions of standard NURBS parameterisations. The project obtained a series of promising and interesting results which include the use of adaptive splines in isogeometric simulations, the characterisation of hierarchial spline spaces, the construction of bases with optimal stability and sparsity properties, as well as algorithms and data structures allowing an efficient implementation. The research activity carried out within the project reflects the interdisciplinary nature of the topic with theoretical and computational issues which range from geometric design to numerical computations. In particular, the main contributions rely on the extension and development of suitable technologies in the context of applied geometry together with the corresponding application algorithms, which are needed to promote the overall geometry-to-analysis vision of the previously mentioned application-oriented context.

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