Reducing computational workload of physical optics scattered fields from quadratic surfaces by the numerical steepest descent path method

In this paper, we propose the numerical steepest descent path (NSDP) method on the complex plane to solve the physical optics (PO) scattered fields from the electrically large quadratic patches. The phase behaviors of PO integrands depict elliptic and hyperbolic on the parabolic and saddle quadratic patches, respectively. On invoking the NSDP method, the contour paths of the surface PO integral are transformed to the NSDPs on the complex plane. Numerical examples for the PO scattered fields from saddle surfaces illustrate that the NSDP method for solving PO scattered fields achieves frequency independent computational effort and error controllable accuracy.