原子位错模拟的高阶边界条件
Higher-Order Boundary Conditions for Atomistic Dislocation Simulations
AI总结：
本研究针对标准超胞方法收敛慢的问题，提出基于多极展开、结合连续介质预测解与离散矩校正的位错原子模拟高阶边界条件，经螺型和刃型位错实验验证收敛速率符合预期，有限尺寸效应低且成本适中。
摘要：
我们提出了一种用于位错原子模拟的高阶边界条件，以解决标准超胞方法收敛缓慢的问题。该方法基于平衡位移的多极展开，将连续介质预测解与离散矩校正相结合。连续介质预测解通过Galerkin谱方法求解一系列奇异椭圆偏微分方程（PDEs）得到，而矩系数则通过力-矩恒等式计算，且近似误差可控。该方法的一个关键特性是精确的连续介质预测解与矩计算之间的耦合，从而能够构建可系统改进的高阶边界条件。我们据此设计了新算法，针对螺型位错和刃型位错的数值结果证实了其在几何范数和能量范数下的预期收敛速率，同时降低了有限尺寸效应且计算成本适中。
英文摘要：
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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