Acoustic scattering by a sound-hard rectangle

Journal article, 1991

The scattering of an incoming plane wave by a sound-hard infinitely thin rectangle is considered. Starting from a double spatial Fourier transform representation of the scattered wave, a matching of the conditions in the plane of the rectangle leads to an integral equation for the potential jump across the rectangle. The jump is expanded in a double series in Chebyshev polynomials which fulfill the right edge conditions (but no special measures are taken for the corners where the right conditions are anyway unknown). The integral equation is thus discretized and the only tricky part is the computations of double integrals in the systen matrix where special care must be excercised. A double stationary phase analysis gives the scattered far fields, and some numerical examples of total scattering cross sections are given.