Computation of elliptic integrals of the third kind in high-frequency EM scattering problems

The expression for the surface-ray fields in the UTD formulation is such that in the computation the antenna characteristics over these scatterers, these elliptic integrals are accessed repeatedly, typically up to 1 million times. Hence, it is desirable to determine the computational efficiency of the various formulae vis-a-vis the nature of the scattering structures. The authors present a comparison of the accuracy, range and computational complexity of the various formulations