Efficient Calculation of the Green's Function for 2-D Periodic Line Sources Using Ewald Method

An accelerated calculation scheme is presented for the Green's function of the two-dimensional (2-D) periodic array of line sources based on the Ewald sum technique. The contour integral representation of the Hankel function and the Poisson sum formula are employed to accelerate the slowly convergent Green's function series. The resulting Green's function is expressed as the sum of an exponential series in the spatial domain and a spectral series consisting of the exponential integral functions, both with Gaussian convergence.