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arXiv · 2510.04751

Higher-Order Boundary Conditions for Atomistic Dislocation Simulations

Xinyi Wei·Julian Braun·Yangshuai Wang·Lei Zhang
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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.

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Xinyi Wei, Julian Braun, Yangshuai Wang, Lei Zhang. 2025-10-06. Higher-Order Boundary Conditions for Atomistic Dislocation Simulations. https://arxiv.org/abs/2510.04751

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