Comparison of parallel-plate Green’s function acceleration techniques

Paper in proceeding, 2012

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.