A high‐order enrichment strategy for the finite cell method. Issue 1 (21st October 2015)

• Record Type: Journal Article
• Authors: Joulaian, Meysam; Zander, Nils; Bog, Tino; Kollmannsberger, Stefan; Rank, Ernst; Düster, Alexander
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 15:Issue 1(2015)
• Page Start: 207
• Page End: 208
• Publication Date: 2015-10-21
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201510094
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: Thanks to the application of the immersed boundary approach in the finite cell method, the mesh can be defined independently from the geometry. Although this leads to a significant simplification of the mesh generation, it might cause difficulties in the solution. One of the possible difficulties will occur if the exact solution of the underlying problem exhibits a kink inside an element, for instance at material interfaces. In such a case, the solution turns out less smooth – and the convergence rate is deteriorated if no further measures are taken into account. In this paper, we explore a remedy by considering the partition of unity method. The proposed approach allows to define enrichment functions with the help of a high‐order implicit representation of the material interface. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)