Open AccessA non-local formulation for level-set modelling
Author(s) -
Stéphane Valance
Publication year - 2012
Publication title -
european journal of computational mechanics
Language(s) - English
Resource type - Journals
eISSN - 2642-2085
pISSN - 2642-2050
DOI - 10.13052/17797179.2012.740588
Subject(s) - curvature , level set method , set (abstract data type) , level set (data structures) , mathematics , simplicity , mathematical optimization , algorithm , computer science , geometry , artificial intelligence , physics , quantum mechanics , image segmentation , programming language , segmentation
The level-set method, as introduced by Osher et al. (Osher, S., & Sethian, J., 1988. Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton–Jacobi formulations. Journal of Computational Physics, 79, 12–49.) presents some flaws with respect to algorithmic simplicity and solution admissibility. In this paper, we present a robust approach for the level-set modelling by taking advantage of readily available work from phase-field framework. By adapting the latter with proper velocity correction, we have obtained a non-local formulation of the level-set problem that overrides the aforementioned problems. An application of this approach, both in explicit finite differences and implicit iso-geometric analysis, illustrates the efficiency of this new formulation.