@Article{CiCP-18-5,
author = {},
title = {A Numerical Scheme for Generalized Peierls-Nabarro Model of Dislocations Based on the Fast Multipole Method and Iterative Grid Redistribution},
journal = {Communications in Computational Physics},
year = {2015},
volume = {18},
number = {5},
pages = {1282--1312},
abstract = {<p style="text-align: justify;">Dislocations are line defects in crystalline materials. The Peierls-Nabarro
models are hybrid models that incorporate atomic structure of dislocation core into
continuum framework. In this paper, we present a numerical method for a generalized
Peierls-Nabarro model for curved dislocations, based on the fast multipole method
and the iterative grid redistribution. The fast multipole method enables the calculation
of the long-range elastic interaction within operations that scale linearly with the
total number of grid points. The iterative grid redistribution places more mesh nodes
in the regions around the dislocations than in the rest of the domain, thus increases
the accuracy and efficiency. This numerical scheme improves the available numerical
methods in the literature in which the long-range elastic interactions are calculated
directly from summations in the physical domains; and is more flexible to handle
problems with general boundary conditions compared with the previous FFT based
method which applies only under periodic boundary conditions. Numerical examples
using this method on the core structures of dislocations in Al and Cu and in epitaxial
thin films are presented.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.130114.270315a},
url = {https://global-sci.com/article/80362/a-numerical-scheme-for-generalized-peierls-nabarro-model-of-dislocations-based-on-the-fast-multipole-method-and-iterative-grid-redistribution}
}