In [A. Capozzoli, C. Curcio, A. Liseno, MMS, Pizzo Calabro, Italy, 2022], the problem of modeling a source/scatterer using an equivalent radiator has been addressed and an approach has been given and numerically assessed.
Once dimensioned the radiating panel, a practical implementation can be provided by a non-uniform array. The element positions should be chosen so that the array is capable to approximate, with an adequate accuracy, the fields radiated by the equivalent radiator. Here, the array element positioning is performed by exploiting a quadrature rule which takes into account that the singular functions supported on the region of interest associated to the most significant singular values of the radiation operator are related to those supported on the equivalent panel by a radiation integral. The quadrature rule enables also to choose a set of weights which are essential in the definition of the element excitation coefficients from the knowledge of the source distribution on the equivalent panel. For simplicity, a one-dimensional problem with a Legendre quadrature rule is considered. The approach is numerically assessed by checking the capability of the array to radiate, with a satisfactory degree of accuracy, the singular functions associated to the region of interest.