Convergence rate for numerical computation of the lattice Green's function

Details Convergence rate for numerical computation of the lattice Green's function Convergence rate for numerical computation of the lattice Green's function

2008-10-31

arxiv.org/abs/0810.5709v1

Phys. Rev. E 79, 037701 (2009)

Physics

Condensed Matter

Materials Science

12 pages, 4 figures

Scientific paper

10.1103/PhysRevE.79.037701

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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