Efficient Evaluation of the Physical-Optics Integrals for Conducting Surfaces Using the Uniform Stationary Phase Method

The computational time to evaluate the physical optics (PO) expression by numerical integration increases rapidly with the increase of electrical size of scattering surfaces. However, the computational time of PO integrals for electrically large object can be greatly reduced by using the stationary phase method, which is independent of the wavenumber. For this method, the theory and numerical implementations for isolated critical points have been well developed. However, for cases of nearby critical points, there are still a few issues to be considered, especially, in numerical implementations. In this paper, we mainly study the numerical implementations for several most common cases of nearby critical points. In particular, the cases of two nearby inner stationary phase points and complex inner stationary phase points are discussed in more details. Such cases occur frequently when the scattering surface includes convex-concave parts, but the numerical implementations to such cases have not been reported to our knowledge. The difficulty lies in how to identify whether two inner stationary points and complex inner stationary points on the surfaces with arbitrary shapes are close to each other or not. A strategy is designed to solve this difficulty. By validation in some typical examples, we find that the stationary phase method is robust enough to evaluate the PO integrals accurately. Finally, some interesting phenomena observed in numerical validations are interpreted.