Scattering by a cylinder: A fast exact numerical solution

The known exact analytic solutions to the problem of (acoustic and electromagnetic) scattering by a two-dimensional infinite right circular cylinder are not in closed form, but consist of infinite series, each term of which contains Hankel and Bessel functions of increasing order, and the convergence rate of which decreases rapidly with increasing (ka) numbers. For a given numerical solution, it is thus necessary to compute many Hankel and Bessel functions in high order for each spatial datum point for which the scattered field need be calculated. Presented is an exact numerical method of solution, which is in closed form, and requires the computation of only one Hankel function of order unity per spatial datum point for which the fields need be calculated. The method consists of a closed form numerical deconvolution solution of the scattering integral equation, executed efficiently with the aid of the fast Fourier transform algorithm, thus requiring only ( (3)/(2) N log2 N) complex arithmetic multiply–add operations, and the computation of only N Hankel functions of order unity, where N is the number of spatial datum points for which a solution is required. Because of the extreme simplicity of the method of solution, a computer program listing for the algorithm is presented. Numerico-experimental results verifying the speed and accuracy of the method are also presented.