A novel approach to accelerate spectral domain approach for shielded microstrip lines using the Levin transformations and summation-by-parts

Abstract

A novel approach, which uses the Levin transformations or the hybrid of the Levin transformations and summation-by-parts, is presented for the acceleration of the slowly convergent series that asymptotically behave as 1/nk and sinusoidal functions divided by nk. This approach does not need the asymptotic expansion for the Green's functions and the Bessel functions, which saves the work for finding the asymptotic expansion coefficients. This approach has been applied to the acceleration of the infinite series summation in the shielded microstrip problem solved by the spectral domain approach (SDA) for obtaining accurate solutions of the propagation constant. Effective criteria of calculating the number of terms used in direct summation before applying the Levin transformations have been developed in this application. This approach can be easily extended to handle the multilayered shielded microstrip structure.