Project Details
Projekt
A posteriori error estimation and local refinement for polytopal meshes based on scaled boundary isogeometric analysis
Applicant
Professor Dr. Bernd Simeon
Subject Area
Mathematics
Applied Mechanics, Statics and Dynamics
Applied Mechanics, Statics and Dynamics
Term
since 2024
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 495926269
This project aims at developing the theoretical underpinnings and the algorithmic machinery for adaptive numerical methods in the context of polytopal meshes that are discretized patch-wise by the scaled boundary method in its isogeometric analysis (IGA) variant. Particular attention will be devoted to the combination of hierarchical B-spline refinement and corresponding residual-type estimators with the special structure of the scaled boundary parametrization. The following objectives are at the core of this proposal: 1) The singularity in the scaling center of a scaled-boundary objects deserves special attention as it comes with a loss of regularity. The first objective consists therefore of a thorough analysis of the asymptotic behavior of discretizations in the vicinity of the scaling center and, if necessary, the development of stabilization techniques to come up with a robust error estimation procedure. 2) Different refinement strategies need to be evaluated and compared in order to come up with a clear conclusion and a powerful and versatile procedure. In this context, one has to consider a multi-block scenario with a number of macro-elements from the very beginning. 3) Concentrating on the concept of residual-type estimators, a tailored error estimation technique needs to be developed that meets the requirements of efficiency and reliability, not only within a star-shaped element but also in the multi-block scenario. 4) Application-oriented examples from solid mechanics shall demonstrate the potential of the adaptive procedures. This includes the transfer to Reissner-Mindlin shells. To achieve these goals, the working group of the applicant draws on strong expertise in isogeometric analysis, in particular in the fields of local refinement and scaled boundary approaches, and computational mechanics. Moreover, a long collaboration record with several of the partners adds to our role as numerical analysis partner in the proposed Focus Group.
DFG Programme
Research Units
