Use of linear and nonlinear algorithms in the acceleration of doubly infinite Green´s function series

It is shown that the application of linear and nonlinear algorithms improves the convergence of the series representing the doubly infinite free-space periodic Green´s function. The numerical results indicate that the algorithms converge faster than the first-order acceleration. Convergence properties of the Green´s function series are reported for the `on plane´ case in which the series has the slowest convergence. The number of terms taken in the series and a relative error measure are given for various values of a convergence factor as the observation point is taken at different locations within a unit cell