Higher-Order Boundary Conditions for Atomistic Dislocation Simulations
Abstract
We present a higher-order boundary condition for atomistic simulations of dislocations that address the slow convergence of standard supercell methods. The method is based on a multipole expansion of the equilibrium displacement, combining continuum predictor solutions with discrete moment corrections. The continuum predictors are computed by solving a hierarchy of singular elliptic PDEs via a Galerkin spectral method, while moment coefficients are evaluated from force-moment identities with controlled approximation error. A key feature is the coupling between accurate continuum predictors and moment evaluations, enabling the construction of systematically improvable high-order boundary conditions. We thus design novel algorithms, and numerical results for screw and edge dislocations confirm the predicted convergence rates in geometry and energy norms, with reduced finite-size effects and moderate computational cost.
Cite
@article{arxiv.2510.04751,
title = {Higher-Order Boundary Conditions for Atomistic Dislocation Simulations},
author = {Xinyi Wei and Julian Braun and Yangshuai Wang and Lei Zhang},
journal= {arXiv preprint arXiv:2510.04751},
year = {2025}
}