# Direct approach to mean-curvature flow with topological changes

Kybernetika (2009)

• Volume: 45, Issue: 4, page 591-604
• ISSN: 0023-5954

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## Abstract

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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 $\Gamma \left(t\right):S\to {ℝ}^{2}$, $t\geqq 0$. 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.

## How to cite

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Pauš, Petr, and Beneš, Michal. "Direct approach to mean-curvature flow with topological changes." Kybernetika 45.4 (2009): 591-604. <http://eudml.org/doc/37721>.

@article{Pauš2009,
abstract = {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.},
author = {Pauš, Petr, Beneš, Michal},
journal = {Kybernetika},
keywords = {mean curvature flow; dislocation dynamics; parametric approach; dislocation dynamics; mean curvature flow; parametric approach; numerical examples; backward Euler; method of lines; numerical stability; algorithm; topological changes},
language = {eng},
number = {4},
pages = {591-604},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Direct approach to mean-curvature flow with topological changes},
url = {http://eudml.org/doc/37721},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Pauš, Petr
AU - Beneš, Michal
TI - Direct approach to mean-curvature flow with topological changes
JO - Kybernetika
PY - 2009
PB - Institute of Information Theory and Automation AS CR
VL - 45
IS - 4
SP - 591
EP - 604
AB - 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.
LA - eng
KW - mean curvature flow; dislocation dynamics; parametric approach; dislocation dynamics; mean curvature flow; parametric approach; numerical examples; backward Euler; method of lines; numerical stability; algorithm; topological changes
UR - http://eudml.org/doc/37721
ER -

## References

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