EXTRAPOLATION METHODS FOR SOMMERFELD INTEGRAL TAILS

A review is presented of the extrapolation methods for accelerating th e convergence of Sommerfeld-type integrals (i.e., semi-infinite range integrals with Bessel function kernels), which arise in problems invol ving antennas or scatterers embedded in planar multilayered media. Att ention is limited to partition-extrapolation procedures in which the S ommerfeld integral is evaluated as a sum of a series of partial integr als over finite subintervals and is accelerated by an extrapolation me thod applied over the real-axis tail segment (a, infinity) of the inte gration path, where a>0 is selected to ensure that the integrand is we ll behaved. An analytical form of the asymptotic truncation error (or the remainder), which characterizes the convergence properties of the sequence of partial sums and serves as a basis for some of the most ef ficient extrapolation methods, is derived. Several extrapolation algor ithms deemed to be the most suitable for the Sommerfeld integrals are described and their performance is compared. It is demonstrated that t he performance of these methods is strongly affected by the horizontal displacement of the source and field points rho and by the choice of the subinterval break points. Furthermore, it is found that some well- known extrapolation techniques may fail for a number of values of rho and ways to remedy this are suggested. Finally, the most effective ext rapolation methods for accelerating Sommerfeld integral tails are reco mmended.