论文标题
晶体缺陷的高阶远场边界条件
Higher-order Far-field Boundary Conditions for Crystalline Defects
论文作者
论文摘要
由于缺陷的存在，晶体材料表现出远程弹性场，从而导致原子模拟中的重要域大小影响。这些远距离字段的严格远场扩展以离散多极项和连续校正器的形式标识了低级结构。我们提出了一种新型的数值方案，该方案利用这种低级结构来通过最大程度地减少域大小效应来加速材料缺陷模拟。我们的方法迭代地改善了边界条件，系统地遵循了远场的渐近扩展。我们为该方法和一系列经验数值测试提供了严格的错误估计，以评估其收敛性和鲁棒性。
Crystalline materials exhibit long-range elastic fields due to the presence of defects, leading to significant domain size effects in atomistic simulations. A rigorous far-field expansion of these long-range fields identifies low-rank structure in the form of a sum of discrete multipole terms and continuum correctors. We propose a novel numerical scheme that exploits this low-rank structure to accelerate material defect simulations by minimizing the domain size effects. Our approach iteratively improves the boundary condition, systematically following the asymptotic expansion of the far field. We provide both rigorous error estimates for the method and a range of empirical numerical tests, to assess it's convergence and robustness.
