长位错的有效柔性边界条件
Efficient flexible boundary conditions for long dislocations
摘要：
我们提出了一种新的有效的实现灵活的边界条件（FBC）的方法，最初提出的辛克莱等人，对于大的单周期问题。效率主要是通过构建一个分层矩阵（$\mathscr{H}$ -矩阵）表示的周期性的格林矩阵，降低了更新的原子问题的边界条件的复杂性，从二次几乎线性的垫原子的数量。此外，我们的实现得到了来自数值分析的各种其他工具的支持，例如基于残差的边界条件变换以加速收敛。我们评估的方法，一套全面的例子，相关的预测力学性能，如屈服强度或延展性，包括位错弓出，位错沉淀相互作用，和位错交叉滑移。我们的分析的主要结果是，FBC方法是强大的，易于使用的，高达两个数量级的效率比目前的最先进的方法，这类问题的周期性位错阵列（PAD）的方法，在所需的数量的每原子力计算时，这两种方法提供类似的精度。这为大规模原子模拟开辟了新的前景-而不必担心困扰经典边界条件的虚假图像效应。
英文摘要：
We present a novel efficient implementation of the flexible boundary condition (FBC) method, initially proposed by Sinclair et al., for large single-periodic problems. Efficiency is primarily achieved by constructing a hierarchical matrix ($\mathscr{H}$-matrix) representation of the periodic Green matrix, reducing the complexity for updating the boundary conditions of the atomistic problem from quadratic to almost linear in the number of pad atoms. In addition, our implementation is supported by various other tools from numerical analysis, such as a residual-based transformation of the boundary conditions to accelerate the convergence. We assess the method for a comprehensive set of examples, relevant for predicting mechanical properties, such as yield strength or ductility, including dislocation bow-out, dislocation-precipitate interaction, and dislocation cross-slip. The main result of our analysis is that the FBC method is robust, easy-to-use, and up to two orders of magnitude more efficient than the current state-of-the-art method for this class of problems, the periodic array of dislocations (PAD) method, in terms of the required number of per-atom force computations when both methods give similar accuracy. This opens new prospects for large-scale atomistic simulations - without having to worry about spurious image effects that plague classical boundary conditions.
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