On appropriate equivalent monopole sets for rigid body scattering problems

The present paper investigates properties of the solutions obtained with the equivalent sources method in scattering problems with the aim of identifying suitable monopole arrangements. Simple geometry scatterers--parallelepipeds with different aspect ratios--are considered and easy-to-implement source supports are tested: linear, circular, elliptical, and a "double linear" one. It was found that the supports providing best solutions differ according to the body geometry and the incidence angle of the impinging wave. Moreover, in the situations in which the other supports fail, it is shown that the double linear one provides satisfactory solutions with a minimum number of monopoles. Rules that furnish appropriate numbers of sources to use as well as their positioning are given for the different cases. A simple procedure based on these rules is proposed for scatterers with a more complex geometry, guaranteeing, still with a low number of monopoles, solutions with satisfactory accuracy.