A finite element method for level sets
Citation for published version (APA):
Valance, S., Borst, de, R., Rethore, J., & Coret, M. (2009). A finite element method for level sets. In J. Eberhardsteiner, C. Hellmich, H. A. Mang, & J. Périaux (Eds.), New Computational Challenges in Materials, Structures, and Fluids : ECCOMAS Multidisciplinary Jubilee Symposium (EMJS 2008), February 18-20, 2008, Vienna, Austria (pp. 95-106). (Computational Methods in Applied Sciences; Vol. 14). Springer.
https://doi.org/10.1007/978-1-4020-9231-2
DOI:
10.1007/978-1-4020-9231-2 Document status and date: Published: 01/01/2009 Document Version:
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A Finite Element Method for Level Sets
S. Valance, R. de Borst, J. R´ethor´e, and M. Coret
AbstractLevel set methods have recently gained much popularity to capture discon-tinuities, including their possible propagation. In this contribution we present a finite element approach for solving the governing equations of level set methods. After a review of the governing equations, the initialisation of the level sets, the discretisa-tion on a finite domain and the stabilisadiscretisa-tion of the resulting finite element method will be discussed. Special attention will be given to the proper treatment of the internal boundary condition, which is achieved by exploiting the partition-of-unity property of finite element shape functions.
Keywords level sets· finite elements · partition of unity · evolving discontinuities
1 Introduction
In the late 1980s, Osher and Sethian [1] have suggested an elegant method to numer-ically model hypersurfaces. The starting point is the definition of a scalar level set functionφ. The zero-isolevel contour of this function describes the hypersurface, while the signed distance provided by the level set function enables the simulation of the evolution of the hypersurface.
Initially, level set methods were applied to the computation of phase changes in flows as driven by a diffusion equation. Subsequent applications have also included weather predictions and image analysis [2]. More recently, they have also been used in conjunction with finite element methods that exploit the partition-of-unity prop-erty of finite element shape functions to capture crack propagation, especially in
S. Valance, J. R´ethor´e, and M. Coret
LaMCoS, UMR CNRS 5514, INSA de Lyon, 69621 Villeurbanne, France R. de Borst
Eindhoven University of Technology, Department of Mechanical Engineering, P.O. Box 513, 5600 MB Eindhoven, The Netherlands; E-mail: r.d.borst@tue.nl
J. Eberhardsteiner et al. (eds.), ECCOMAS Multidisciplinary Jubilee Symposium, Computational Methods in Applied Sciences.
c
Springer Science + Business Media B.V. 2009
