Application of Kummer´s Transformation to the Efficient Computation of the 3-D Green´s Function With 1-D Periodicity

The 3-D homogeneous Green´s function with 1-D periodicity is commonly expressed as spatial and spectral infinite series that may show very slow convergence. In this work Kummer´s transformation is applied to the spatial series in order to accelerate its convergence. By retaining a sufficiently large number of asymptotic terms in the application of Kummer´s transformation, the spatial series is split into a set of series which can be accurately obtained with very low computational effort. The numerical results obtained show that, when the number of asymptotic terms retained in Kummer´s transformation is large enough, the convergence acceleration method proposed in this work is always faster than existing acceleration methods such as the spectral Kummer-Poisson´s method and Ewald´s method.