Flexible boundary condition methods couple an isolated defect to bulk through the bulk lattice Greens function. The inversion of the force-constant matrix for the lattice Greens 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 Greens 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 Greens function.
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