An algebraic calculation method for the acoustic low frequency expansion

In the present work we propose an analytical method for the algebraic calculation of the low frequency expansion of the solution of a scalar scattering problem upon a smooth starshaped scatterer. The method is based on the far field expansion theorem, introduced by Atkinson and Wilcox in the middle of the last century, applied in the low frequency realm. In this view, the need for solving elliptical boundary value problems to obtain the low frequency approximations is replaced by an analytical procedure, easily encoded in an algorithm including only algebraic operators. As a demonstration example, the method is applied to the acoustic scattering problem with plane wave excitation upon three different non-penetrable spherical scatterers. The first low frequency approximations are deduced, yielding the validity of the proposed method by both recovering already known results and accurately deriving higher orders of approximation.