格点格林函数数值计算的收敛速度
Convergence rate for numerical computation of the lattice Green's function
摘要：
柔性边界条件方法通过体晶格格林函数将孤立缺陷耦合到体。格点格林函数的力常数矩阵的反演需要傅立叶技术来投影出奇异子空间，对应于无限格点的均匀位移和力。三种不同的技术--相对位移、弹性格林函数和不连续性校正--对于指定的数值误差具有不同的计算复杂度。我们计算了弹性各向同性和各向异性的情况下的收敛速度，并将它们与分析结果进行比较。我们的研究结果证实，不连续性校正是计算效率最高的方法来计算格点格林函数。
英文摘要：
Flexible boundary condition methods couple an isolated defect to bulk through the bulk lattice Green's function. The inversion of the force-constant matrix for the lattice Green's function requires Fourier techniques to project out the singular subspace, corresponding to uniform displacements and forces for the infinite lattice. Three different techniques--relative displacement, elastic Green's function, and discontinuity correction--have different computational complexity for a specified numerical error. We calculate the convergence rates for elastically isotropic and anisotropic cases and compare them to analytic results. Our results confirm that the discontinuity correction is the most computationally efficient method to compute the lattice Green's function.
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