## 1 Introduction  
The latest advances in the development of integrated circuit technology have increased the attractivity of microstrip transmission lines for the realization of high-speed interconnects in monolithic microwave and millimeter waves integrated circuits (MIMICs). In this contest, the width and the thickness of the metallic region can be comparable, and the transverse cross-section is closed to a trapezoidal shape due to the etching undercuts, or because of the electrolytical growth process. For all these reasons, the classical approaches, based on the modeling of the metallic region as a zero-thickness flat strip, are inappropriate for an accurate analysis of the propagation. Great attention has been paid in the last few decades to developing techniques which are able to evaluate the effect of the thickness and the cross-sectional shape of the metallic strip on the propagation [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]. Among others, integral equation formulations have been widely preferred. In order to search for the solution of an integral equation which cannot be expressed in a closed form, a discretization scheme has to be provided. On the other hand, it is well-known that a direct discretization can lead to ill-conditioned and/or dense matrices for which the convergence of the approximate solution to the exact one, if it exists, cannot be guaranteed. A possible way to overcome this problem is the use of compression techniques [11; 12], the Nystrom method [13; 14], or the direct formulation of the problem in terms of a Fredholm second-kind integral equation [15], just to give some examples. In a recent paper [16], the analysis of bound and leaky modes propagation in single and coupled polygonal cross-section microstrip lines was carried out by generalizing the techniques presented in Refs. [17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30] for the analysis of propagation, radiation and scattering problems. The problem has been formulated as a homogeneous one-dimensionalelectric field integral equation (EFIE) in the spectral domain. A converging matrix equation has been achieved by means of the method of analytical preconditioning (MAP) [31], i.e., the Galerkin method, with suitable expansion functions such that [PERSON]'s theorems can be applied [32]. In Ref. [16], this goal was reached by selecting expansion functions with a closed form Fourier transform reconstructing the physical behavior of the unknowns, even on the wedges. As a result, just a few expansion functions are enough to reconstruct the solution with good accuracy. Moreover, the Galerkin projection integrals have been written in closed form, thus leading to coefficient matrix elements expressed as combinations of one-dimensional integrals over the selected inverse Fourier transform integration path. Unfortunately, the numerical evaluation of the coefficient matrix elements is burdensome. Since the expansion functions are continuous functions defined on finite supports, their spectral domain counterparts are oscillating functions with an algebraic asymptotic decay along the inverse Fourier transform integration path. For this reason, the coefficient matrix elements are improper integrals whose integrands are oscillating functions, which can have a slow asymptotic decay. As such, the simulations can be time-consuming when highly accurate solutions are searched for. A classical way to overcome this problem is the extraction of suitable asymptotic contributions from the integrands, such that the integrals of the extracted contributions can be expressed in closed form [33; 34; 35]. Unfortunately, such a technique leads to accelerated integrands with a faster but still algebraic decay, and it does not modify the asymptotic oscillating behavior of the integrands themselves. As a result, a slower and slower numerical convergence is expected as the accuracy required for the solution increases. Recently, a different perspective was proposed in Refs. [36; 37; 38; 39; 40; 41; 42; 43].