Computation of physical optics integral by Levin´s algorithm on NURBS

Non-Uniform Rational B-Splines (NURBS) are very powerful modeling tools for geometric design due to several reasons including fast and numerically stable algorithms and unified mathematical basis for representing complex objects [1]. Although target modeling is easy with NURBS, applying some numerical tools directly on NURBS is not so straightforward. Since the surface point function and derivative computation is simpler for rational Bezier surfaces (RBS), NURBS surfaces are converted to RBS by Cox-de Boor Algorithm for numerical implementations [2]. Therefore, solving a problem for RBS corresponds to solving it for NURBS surfaces. Indeed, in this paper, RBS are used for surface modeling and radar cross section (RCS) computations. The RCS computations are performed by employing Physical Optics (PO) approximation which is accurate at high frequency regions [3]. Although PO is a more efficient technique for scattering problems at high frequencies, when compared to full-wave techniques, it may be intractable due to rapid oscillations of the PO integral. In the literature, there are several methods to handle the oscillatory integrals including the stationary phase method, which is already applied to PO computations on NURBS surfaces [2, 4]. Another method proposed for highly oscillatory integrals is the Levin´s method which was previously applied to PO problems, particularly RCS computation of targets modeled by quadrilaterals [5]. In this paper, the same approach is utilized on RBS.