A fast exact numerical solution for the acoustic response of concentric cylinders with penetrable interfaces

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 log₂N) algebraic operations, where N is the maximum number of discretization points along the circumference of the cylinder.