Abstract
A fast exact numerical algorithm is presented that computes the line source acoustic response of concentric cylinders filled with acoustic material of contrasting impedances. The fast exact numerical method solves a cylinder scattering problem by a boundary integral equation method. By azimuthal symmetry, the discrete approximation of these integral equations are discrete periodic convolutions with respect to the angular variable. Application of a discrete Fourier transform reduces the boundary integral equations to a system of linear algebraic equations. The response is economically computed by algebraic division and an inverse fast Fourier transform. The dominant cost per temporal frequency is O(N log2 N) algebraic operations, where N is the maximum number of discretization points along the circumference of the cylinder.