An iterative solution to acoustic scattering by rigid objects

Abstract

The scattering problem is formulated as a boundary integral equation over the scattering surface that, through the use of a modified Green’s function, is uniquely solvable for all wavenumbers of interest. This integral equation is further transformed, by operating with the adjoint, into a self-adjoint equation into which a parameter has been introduced by adding and subtracting multiples of the identity. This equation is discretized and is solved in a Neumann series that has been shown to converge, with a suitable choice of the parameter, with no restriction on the wavenumber. Numerical results from several examples—spheres, spheroids, and finite cylinders—are presented and shown to be in complete agreement with those obtained using T-matrix methods. Results of a numerical experiment are presented that show how the parameter choice affects the rate of convergence.