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| HAL: hal-00415902, version 2 |
| DOI: 10.1137/090770862 |
| Detailed view |  Export this paper |
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| SIAM Journal on Numerical Analysis 49, 6 (2011) 2470-2500 |
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| Available versions: | v1 (2009-09-11) | v2 (2009-09-12) |
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| A Generalized Fast Marching Method for dislocation dynamics |
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| Elisabetta Carlini 1Nicolas Forcadel 2 |
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| (2011) |
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| 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 $\mathbb R^N$ (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 $N=2$. |
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| 1: | Dipartimento di Matematica "Guido Castelnuovo" [Roma I] |
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Universita di Roma "La Sapienza" |
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| 2: | CEntre de REcherches en MAthématiques de la DEcision (CEREMADE) |
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CNRS : UMR7534 – Université Paris IX - Paris Dauphine |
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| 3: | Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique (CERMICS) |
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INRIA – Ecole des Ponts ParisTech |
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| Subject | : | Mathematics/Numerical Analysis Mathematics/Analysis of PDEs |
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| Hamilton-Jacobi equations – fast marching scheme – convergence – viscosity solutions – dislocation dynamics – non-local equations. |
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| hal-00415902, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00415902 | |
| oai:hal.archives-ouvertes.fr:hal-00415902 | |
| From: Nicolas Forcadel | |
| Submitted on: Friday, 11 September 2009 20:19:08 | |
| Updated on: Thursday, 22 December 2011 10:41:42 | |
