Efficient Algorithm for the Evaluation of the Physical Optics Scattering by NURBS Surfaces With Relatively General Boundary Condition

An adaptive integration algorithm is presented for the computation of the Physical Optics (PO) electric and magnetic field scattered by electrically large objects modeled by Non-Uniform Rational B-Splines (NURBS). The algorithm is the customization of a more general-purpose result that has been recently published. By using a unique formulation both impenetrable (e.g., impedance surfaces, coated conductors) as well as transparent thin sheet materials (e.g., thin dielectric panels, or frequency selective surfaces) are treated, via their Fresnel reflection and transmission coefficients. The PO radiation integral is evaluated over the NURBS parametric domain. Since most of the computer-aided geometric design (CAGD) tools are based on NURBS, the proposed algorithm allows a straightforward electromagnetic analysis of the structures by exploiting the standard available geometrical description, with no need of generating new geometrical models. Furthermore, the proposed adaptive sampling requires a number of integration points that is found to be drastically smaller than that resulting from standard Nyquist-based sampling integration algorithms. Such reduction of the sampling points is achieved by resorting to high-frequency technique concepts and allows a significant reduction of the CPU computational burden. Therefore the algorithm is efficient and particulary suitable for the electromagnetic characterization of real-life electrically large objects.