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, which is a new 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 PDE problem under consideration. Isogeometric analysis was first proposed by Professor T. Hughes (UT Austin, USA) and his colleagues in 2005, and since then has rapidly attracted substantial interest, especially, in the engineering community. In the core of our interests are:
- Efficiency issues and exploitation of the tensor-product structure
- Multi-patch spline representations and adaptivity in isogeometric spline spaces
- Robust and efficient implementation of isogeometric methods as open-source code