Higher-Order Boundary Conditions for Atomistic Dislocation Simulations
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909826796224512 |
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| author | Wei, Xinyi Braun, Julian Wang, Yangshuai Zhang, Lei |
| author_facet | Wei, Xinyi Braun, Julian Wang, Yangshuai Zhang, Lei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04751 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher-Order Boundary Conditions for Atomistic Dislocation Simulations Wei, Xinyi Braun, Julian Wang, Yangshuai Zhang, Lei Numerical Analysis Computational Physics 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. |
| title | Higher-Order Boundary Conditions for Atomistic Dislocation Simulations |
| topic | Numerical Analysis Computational Physics |
| url | https://arxiv.org/abs/2510.04751 |