  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.
