Our research is devoted to the interaction of applied geometry, which deals with questions of size and shape, and numerical simulation, which is concerned with discretization and approximation methods as well as their efficient implementation.

In particular, we focus on geometric problems arising in the context of isogeometric analysis (IGA), which is an innovative numerical technique that uses splines or NURBS, normally used in CAD (computer aided design), for both representing the geometry of the computational (physical) domain and approximating the solution of the PDE problem under consideration. This property of isogeometric analysis makes it well suited for many applications, where an accurate representation of the geometry is important. Our main interests are:

• Multi-patch discretizations, unstructured spline spaces and manifold splines for IGA
• Adaptivity in IGA and high-order FEM
• Problem-specific optimization of isogeometric discretizations
• Spline-based constructions for thin shells
• Robust and efficient isogeometric solvers