The stationary phase method is used to calculate the radiation pattern of antennas on complex structures. Physical optics (PO) approximation has been applied for the induced currents. The problem is stated directly over the parametric surfaces used to model the geometry and no translation of geometrical formats is required. The integral comes from the contribution of certain points on the surface (specular, boundary and vertices) where the phase term of the integrand presents a stationary behavior. In general, the asymptotic integration behaves similar to the numerical one but being more efficient in execution time than the latter.
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Conde et al. (2001) studied this question.
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