Geodesic
Direct approach to mean-curvature flow with topological changes
Kybernetika, Tome 45 (2009) no. 4, pp. 591-604.

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This contribution deals with the numerical simulation of dislocation dynamics. Dislocations are described by means of the evolution of a family of closed or open smooth curves $ \Gamma (t) : S \rightarrow \mathbb{R} ^2 $, $ t \geqq 0 $. The curves are driven by the normal velocity $v$ which is the function of curvature $\kappa$ and the position. The evolution law reads as: $v = -\kappa + F$. The motion law is treated using direct approach numerically solved by two schemes, i. e., backward Euler semi-implicit and semi-discrete method of lines. Numerical stability is improved by tangential redistribution of curve points which allows long time computations and better accuracy. The results of dislocation dynamics simulation are presented (e. g., dislocations in channel or Frank–Read source). We also introduce an algorithm for treatment of topological changes in the evolving curve.
Classification : 35L65, 53C44, 74E15, 74H15, 74S10, 76M12, 80A20
Keywords: mean curvature flow; dislocation dynamics; parametric approach 
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     author = {Pau\v{s}, Petr and Bene\v{s}, Michal},
     title = {Direct approach to mean-curvature flow with topological changes},
     journal = {Kybernetika},
     pages = {591--604},
     publisher = {mathdoc},
     volume = {45},
     number = {4},
     year = {2009},
     mrnumber = {2588625},
     zbl = {1192.65128},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2009__45_4_a3/}
}
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Pauš, Petr; Beneš, Michal. Direct approach to mean-curvature flow with topological changes. Kybernetika, Tome 45 (2009) no. 4, pp. 591-604. http://geodesic.mathdoc.fr/item/KYB_2009__45_4_a3/