"Isogeometric analysis (IA), which was introduced in 2005 by Tom Hughes et al., is a novel technique for numerical simulation which uses the same spaces of functions for the representation of the geometry and for the numerical simulation. It has the potential of closing the gap between numerical simulation and computer aided design, which is caused by the different representations of geometry (piecewise linear vs. rational splines = NURBS). This gap is currently a bottleneck in the design process, since the design and the numerical simulation phase cannot be connected in a seamless fashion, but only through time-consuming conversion processes.The application of IA leads to new challenging problems for geometric design, which are related to the representation of computational domains by NURBS parameterizations. The project will address some of them.More precisely, it will discuss computational methods for generating NURBS parameterizations for several classes of computational domains, such as CSG models, general CAD models, and domains obtained from medical data. It will also analyze the quality of these parameterizations with respect to the distribution of singularities and with respect to the distortion which is introduced by the parameterization. Additional points of interest are the construction of locally refinable spaces of test functions for IA, which are compatible with NURBS parameterizations and support both h-refinement (knot insertion) and p-refinement (degree elevation), domain decomposition techniques and design optimization.These three topics will be analyzed in close connection to related applications to numerical optimization and to shape optimization. The execution of the project requires the combination of knowledge available at the host institution with the expertise of some of its European partners, as well as the profound education of the fellow in Computer Science and Applied Mathematics."