Accurate evaluation of Sommerfeld integrals using the fast Fourier transform

It is shown that the fast Fourier transform (FFT) combines naturally with Simpson´s rule for Sommerfeld-type integral computation. The principal advantage of using the FFT is that a single subroutine call yields a set of sample values of an integral (i.e. the integral for various values of an integrand parameter). Such samples could be useful in themselves. In other applications Sommerfeld integrals represent Green´s functions nested within other spatial integrals, so samples from the FFT might be useful in approximating the outernested integral. Several examples are provided to illustrate the process.<>