Projects

Isogeometric XFEM

In this project, we investigate the coupling of Isogeometric Analysis with the Extended Finite Element Method (XFEM). Isogeometric Analysis is a recently developed computational approach that aims to unify the field of Computer-Assisted Design (CAD) with Finite Element Analysis. The main idea of this method is to use the same functions employed in CAD (such as B-Splines or Non-Uniform Rational B-Splines) for the analysis and the solution of partial differential equations. Advantages of this method include exact representation of complex geometric domains for even coarse meshes, higher regularity (i.e. smoothness) of the solution, and higher order approximation compared to standard finite elements.

XFEM is a well-known method for modeling discontinuities (such as cracks, material interfaces, voids, and inclusions) through the approximation space used in analysis. The advantage of this method is that it does not require a matching discretization (mesh ) of the problem domain. The Goal of this project is to combine XFEM with Isogemetric Analysis, resulting in a new method that inherits the advantages from both approaches.