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A Generalized Fast Marching Method for Dislocation Dynamics
2011
SIAM Journal on Numerical Analysis
In this paper, we consider a Generalized Fast Marching Method (GFMM) as a numerical method to compute dislocation dynamics. The dynamics of a dislocation hyper-surface in R N (with N = 2 for physical applications) is given by its normal velocity which is a non-local function of the whole shape of the hyper-surface 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.
doi:10.1137/090770862
fatcat:qli66i6s6jglncduhxzcue6xza