EFFICIENT COMPUTATION OF THE FREE-SPACE PERIODIC GREEN-FUNCTION

The application of Shanks's transform is shown to improve the convergence of the series representing the doubly infinite free-space periodic Green's function. Higher order Shanks transforms are computed via Wynn's epsilon-algorithm. Numerical results confirm that a dramatic improvement in the convergence rate is obtained for the "onplane" case, in which the series converges extremely slowly. In certain instances, the computation time can be reduced by as much as a factor of a few thousands. A relative error measure versus the number of terms taken in the series is plotted for various values of a convergence factor as the observation point is varied within a unit cell. Computation times are also provided.