Case study about the accuracy behavior of three different T-matrix methods

In this paper we discuss the influence of two different sets of weighting functions on the accuracy behavior of T-matrix calculations for scalar scattering problems. The first set of weighting functions is related to one of Waterman's original approaches. The other set results into a least-squares scheme for the transmission problem. It is shown that both sets of weighting functions produce results with a converse accuracy behavior in the near and far fields. Additional information, such as reciprocity and the fulfillment of the boundary condition, are needed to choose the set of weighting functions that is most appropriate for a certain application. The obtained criteria are applied afterward to an iterative T-matrix approach we developed to analyze scattering on regular particle geometries with an impressed but slight surface irregularity. However, its usefulness is demonstrated in this paper by analyzing the far-field scattering behavior of Chebyshev particles of higher orders.