Accelerating the Evaluation of Series Representing the 2-D Periodic Green’s Function

The free space Green's function with 2-D periodicity usually show very slow convergence owing to unavoidable singularities in the reciprocal solution domain. Particularly, the spatial domain Green's function doesn't convergence at all when the source point is in the same domain as the observation point. A method is discussed to effectively improve the slow convergence by using the Ewald method and summing in a combination of spectral and spatial expression. Numerical results demonstrate that the transform converges rapidly than the direct original summation series.