Midpoint Summation: A Method for Accurate and Efficient Summation of Series Appearing in Electromagnetics

A novel approach for fast approximation of a summation to an integral with midpoint summation (MPS) has been developed, which requires one term less than the existing Euler-Maclaurin formula (EMF) for obtaining the same order of accuracy. Also, a recursive relation to evaluate the coefficients has been derived. The approach has been applied to the acceleration of the infinite series summation in the shielded microstrip problem using the spectral domain approach (SDA) for obtaining accurate solution to the propagation constant. The speedup in evaluating the elements of the Galerkin matrix is achieved by asymptotic expansions for the Green's function and the Bessel's function and approximating the infinite summation using MPS. Thus, there is no need for evaluating complex coefficients or numerical integration.