Comparison of parallel-plate Green´s function acceleration techniques

A comparative study of acceleration methods for computing the infinite series summation arising in parallel-plate Green´s functions is performed. The spectral summation, the application of the Shanks-transformed spatial summation, and the Ewald method are examined. Results are presented which show that, although the convergence rates of Ewald´s method and the spectral summation are generally largest (i.e. less number of terms), the total series evaluation time for reaching a certain specified accuracy - which is ultimately of more practical importance - is shortest for the Shanks accelerated spatial summation for most of the cases we considered.