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A high‐order enrichment strategy for the finite cell method
Author(s) -
Joulaian Meysam,
Zander Nils,
Bog Tino,
Kollmannsberger Stefan,
Rank Ernst,
Düster Alexander
Publication year - 2015
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201510094
Subject(s) - partition of unity , finite element method , partition (number theory) , convergence (economics) , representation (politics) , rate of convergence , order (exchange) , computer science , boundary (topology) , mathematics , mathematical optimization , topology (electrical circuits) , mathematical analysis , structural engineering , engineering , combinatorics , computer network , channel (broadcasting) , law , economics , economic growth , finance , politics , political science
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)