Seminars at the Faculty of Informatics

Hierarchical refined NURBS and domain decomposition problems

The Faculty of Informatics is pleased to announce a seminar given by Christian Hesch

DATE: Monday, June 23 2014
PLACE: USI Lugano Campus, room SI-008, Informatics building (Via G. Buffi 13)
TIME: 14.00

Actual developments for the numerical treatment of sharp interfaces as they arise in the context of fracture mechanics and phase separation problem are based on regularisation techniques. In particular, phase-field methods have been applied successfully to these problems, using Allen-Cahn type equations as well as Cahn-Hilliard type equations for the additional fields.
In this talk, we will first introduce the applications and - based on the arising continuity requirements - provide a suitable functions space in the context of isogeometric analysis (IGA) using Non-Uniform B-Splines (NURBS) as shape functions. Several drawback will be addressed in the following:

  • How to deal with local refinement? Multivariate B-Splines are defined based on a tensor product of univariate B-Splines. T-Splines can be considered as the IGA counterpart of hanging nodes and provide only C0 continuity. Therefore, we will introduce the concept of hierarchical refined NURBS.
  • How to deal with non-conforming domain decomposition problems? A first mortar based approach for domain decomposition is given in [1] and has been extended to thermomechanical contact, see [2]. The approach rests on a linear interpolation of the dual field, providing only C0 continuity at the interface, i.e. we can not apply standard concepts to systems with higher requirements.

Possible solutions will be discussed within the framework of hierarchical refined NURBS.

HOST: Prof. Rolf Krause