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A Generalized Fast Marching Method for Dislocation Dynamics

Carlini, Elisabetta; Forcadel, Nicolas; Monneau, Régis (2011), A Generalized Fast Marching Method for Dislocation Dynamics, SIAM Journal on Numerical Analysis, 49, 6, p. 2470-2500. http://dx.doi.org/10.1137/090770862

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00415902
Date
2011
Journal name
SIAM Journal on Numerical Analysis
Volume
49
Number
6
Publisher
SIAM
Pages
2470-2500
Publication identifier
Metadata
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Author(s)
Carlini, Elisabetta
Forcadel, Nicolas cc
Monneau, Régis
Abstract (EN)
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 $N=2$.
Subjects / Keywords
Hamilton-Jacobi equations; fast marching scheme; convergence; viscosity solutions; dislocation dynamics; nonlocal equations