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Adaptive anisotropic integration scheme for high‐order fictitious domain methods: Application to thin structures
Author(s) -
Legrain G.,
Moës N.
Publication year - 2018
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5769
Subject(s) - domain (mathematical analysis) , finite element method , curvature , polygon mesh , computer science , estimator , scheme (mathematics) , anisotropy , mathematical optimization , surface (topology) , algorithm , topology (electrical circuits) , mathematics , geometry , mathematical analysis , physics , optics , statistics , combinatorics , computer graphics (images) , thermodynamics
Summary A novel integration scheme is proposed for fictitious domain finite element methods. It relies on the use of a surface tracking strategy based on anisotropic mesh adaptation. Thanks to an error estimator, the method builds iteratively an adapted anisotropic mesh that is refined near the geometrical interface and elongated in the direction of a small curvature. This strategy allows to decrease the integration cost, which can be problematic for high‐order fictitious domain methods. In addition, it opens the possibility for the creation of unfitted solid shell strategies that can be used for the treatment of thin structures. Numerical studies show that the method leads to promising results for both integration cost and behavior with respect to locking.