A GENERALIZED FAST MARCHING METHOD FOR DISLOCATION DYNAMICS

被引：9
|
作者：
Carlini, Elisabetta [1 ]
Forcadel, Nicolas [2 ]
Monneau, Regis [3 ]
机构：
[1] Univ Roma La Sapienza, Dipartimento Matemat, I-00185 Rome, Italy
[2] Univ Paris 09, UMR CNRS 7534, CEREMADE, F-75775 Paris 16, France
[3] Univ Paris Est, Ecole Ponts, F-77455 Marne La Vallee, France
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 2011年 / 49卷 / 06期
关键词：
Hamilton-Jacobi equations; fast marching scheme; convergence; viscosity solutions; dislocation dynamics; nonlocal equations; LEVEL SET METHOD; UNIQUENESS; EXISTENCE; EQUATIONS; VELOCITY; SCHEME;
D O I：
10.1137/090770862
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：2470 / 2500
页数：31
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