Poisson equation with periodic boundary conditions: Multipole-expansion solution

A multipole-expansion approach is given for solving the Poisson equation with periodic boundary conditions by using the (point-group) symmetry of the unit cell and the evaluation of lattice sums (i.e., the lattice Fourier transform). The accuracy of this approach is checked for a highly anisotropic soluble case as well as for the classical example of Cu. Numerical results for Cu show a drastic decrease of the computational time in comparison with the approach used in the full-potential linearized-augmented-plane-wave method.