@Article{CiCP-32-671,
author = {Hodapp , M.},
title = {Efficient Flexible Boundary Conditions for Long Dislocations},
journal = {Communications in Computational Physics},
year = {2022},
volume = {32},
number = {3},
pages = {671--714},
abstract = {<p style="text-align: justify;">We present a novel efficient implementation of the flexible boundary condition (FBC) method, initially proposed by Sinclair et al., for large single-periodic
problems. Efficiency is primarily achieved by constructing a hierarchical matrix ($\mathscr{H}$-matrix) representation of the periodic Green matrix, reducing the complexity for updating the boundary conditions of the atomistic problem from quadratic to almost
linear in the number of pad atoms. In addition, our implementation is supported by
various other tools from numerical analysis, such as a residual-based transformation
of the boundary conditions to accelerate the convergence. We assess the method for
a comprehensive set of examples, relevant for predicting mechanical properties, such
as yield strength or ductility, including dislocation bow-out, dislocation-precipitate interaction, and dislocation cross-slip. The main result of our analysis is that the FBC
method is robust, easy-to-use, and up to two orders of magnitude more efficient than
the current state-of-the-art method for this class of problems, the periodic array of
dislocations (PAD) method, in terms of the required number of per-atom force computations when both methods give similar accuracy. This opens new prospects for
large-scale atomistic simulations — without having to worry about spurious image
effects that plague classical boundary conditions.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2021-0157},
url = {http://global-sci.org/intro/article_detail/cicp/21042.html}
}