Double exponential quadrature formulas for the direct calculation of Sommerfeld integral tails

A novel algorithm for efficient direct integration of Sommerfeld integral (SI) tails arising in the numerical analysis of antennas and scatterers embedded in multilayered media, is presented based on double-exponential (DE) quadrature formulas. When compared to the so-called partition-extrapolation methods, which are traditionally employed for this type of problems, DE quadrature formulas maintain very high accuracy and show error controllable features, while reducing significantly the computational time. Moreover, this fully numerical scheme is very easy to implement, since the associated weights and abscissas can be precomputed.