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.
A generalized fast marching method for dislocation dynamics / Carlini, Elisabetta; Nicolas, Forcadel; Régis, Monneau. - In: SIAM JOURNAL ON NUMERICAL ANALYSIS. - ISSN 0036-1429. - STAMPA. - 49:6(2011), pp. 2470-2500. [10.1137/090770862]
A generalized fast marching method for dislocation dynamics
CARLINI, Elisabetta;
2011
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 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
