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Journal Article

A GENERALIZED FAST MARCHING METHOD FOR DISLOCATION DYNAMICS

ELISABETTA CARLINI, NICOLAS FORCADEL and RÉGIS MONNEAU
SIAM Journal on Numerical Analysis
Vol. 49, No. 5/6 (2011), pp. 2470-2500
Stable URL: http://www.jstor.org/stable/41582702
Page Count: 31
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A GENERALIZED FAST MARCHING METHOD FOR DISLOCATION DYNAMICS
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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 R N (with TV = 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.

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