Discretization Methods: Isogeometric Finite Element Method

Anh-Tu Vuong and Philipp Farah

Whereas creating a Lagrangean finite element mesh only approximates the CAD (Computer Aided Design) geometry and consequently introduces numerical errors, Isogeometric finite elements are an exact representation of the desired geometry. Therefore, Isogeometric finite element methods like Non-Uniform Rational B-Splines (NURBS) or T-Splines have become a great topic of research over the last years.

Applications for Isogeometric finite elements at the Institute for Computational Mechancis are interface- and volume-coupled Fluid-Structure-Interactions as well as smooth contact formulations. Therein, the higher global continuity of Isogeometrics compared to Lagrangean shape functions is a major advantage. For porous media problems NURBS shape functions are applied to fulfill higher compatibility requirements, whereas for contact applications a smooth geometry representation guarantees physically correct interface tractions.