The summation-by-parts algorithm-a new efficient technique for the rapid calculation of certain series arising in shielded planar structures

This paper presents a new technique for the convergence acceleration of a large class of series often arising in electromagnetic problems. The technique is based on the recursive application of the integration-by-parts technique to discrete sequences, thus the given name of the "summation-by-parts" technique. It is shown that the new technique greatly enhances the convergence rate of the series treated, and very small relative errors are obtained by performing a few simple operations. The new technique is applied to the efficient numerical calculation of the Green's functions in a parallel-plate waveguide.