@Article{CiCP-35-273,
author = {Qin , XiaoxueNgan , Alfonso H.W. and Xiang , Yang},
title = {A Threshold Dislocation Dynamics Method},
journal = {Communications in Computational Physics},
year = {2024},
volume = {35},
number = {2},
pages = {273--312},
abstract = {<p style="text-align: justify;">The Merriman-Bence-Osher threshold dynamics method is an efficient algorithm to simulate the motion by mean curvature. It has the advantages of being easy
to implement and with high efficiency. In this paper, we propose a threshold dynamics method for dislocation dynamics in a slip plane, in which the spatial operator is
essentially an anisotropic fractional Laplacian. We show that this threshold dislocation dynamics method is able to give two correct leading orders in dislocation velocity,
including both the $\mathcal{O}(log ε)$ local curvature force and the $\mathcal{O}(1)$ nonlocal force due to
the long-range stress field generated by the dislocations as well as the force due to the
applied stress, where $ε$ is the dislocation core size, if the time step is set to be $∆t = ε.$ This generalizes the available result of threshold dynamics with the corresponding
fractional Laplacian, which is on the leading order $\mathcal{O}(log \Delta t)$ local curvature velocity
under the isotropic kernel. We also propose a numerical method based on spatial variable stretching to correct the mobility and to rescale the velocity for efficient and accurate simulations, which can be applied generally to any threshold dynamics method.
We validate the proposed threshold dislocation dynamics method by numerical simulations of various motions and interaction of dislocations.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2023-0188},
url = {http://global-sci.org/intro/article_detail/cicp/22942.html}
}