A GENERALIZED FAST MARCHING METHOD FOR DISLOCATION DYNAMICS

作者：Carlini Elisabetta^*; Forcadel Nicolas; Monneau Regis

来源：SIAM Journal on Numerical Analysis, 2011, 49(6): 2470-2500.

DOI：10.1137/090770862

• Hamilton-Jacobi equations
• fast marching scheme
• convergence
• viscosity solutions
• dislocation dynamics
• nonlocal equations

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 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.

• 出版日期2011