For non-smooth solution characteristics the finite element approximation is enhanced by special shape functions leading to the extended finite element method (XFEM). The shape M of the shape functions is given in terms of the signed distance function for strong and weak discontinuities. The signed distance function defines the position of the surface between different materials at its zero level. Using the XFEM plane contacts between interacting structures are described in space and time.
For applying the XFEM, the position of the integration points hat to be determined in finite elements, intersected by the separating surface. Therefore, efficient algorithms tessellating intersected finite elements are developed. The picture below shows a tessellation of a hexahedron and the position of the integration points.
Furthermore, for the investigation of two-fluid-flows, an algorithm tessellating four-dimensional space-time finite elements is provided. The movement of a free surface in a four-dimensional space-time finite element in shape of a tesseract is displayed above.
Current Research Projects
S. Reinstädler: Modellierung und numerische Simulation von Hangrutschungen
Completed Research Projects
F. Pasenow: Modellierung oberflächengekoppelter Mehrfeldsysteme und numerische Analyse rutschender Bodenmaterialien, Dissertation, TU Braunschweig, 2014
A. Kölke: Modellierung und Diskretisierung bewegter Diskontinuitäten in randgekoppelten Mehrfeldsystemen, Dissertation, TU Braunschweig, 2005