A Generalized Fast Marching Method for Dislocation Dynamics

Authors:
Elisabetta Carlini;Nicolas Forcadel;Régis Monneau
Affiliations:
carlini@mat.uniroma1.it;forcadel@ceremade.dauphine.fr;monneau@cermics.enpc.fr
Venue:
SIAM Journal on Numerical Analysis
Year:
2011

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Abstract

In this paper, we consider a generalized fast marching method (GFMM) as a numerical method to compute dislocation dynamics. The dynamics of a dislocation hypersurface in $\mathbb{R}^N$ (with $N=2$ for physical applications) is given by its normal velocity which is a nonlocal function of the whole shape of the hypersurface itself. For this dynamics, we show a convergence result of the GFMM as the mesh size goes to zero. We also provide some numerical simulations in dimension $N=2$.