Physical optics integrals evaluation using closed-form expressions and triangular boundary-rectangular mesh algorithm

In this study, the authors propose a novel Filon-type integration method that uses error-controllable and frequency-independent closed-form expression to evaluate highly oscillatory physical optics (PO) surface integrals on smooth conducting surfaces. In this method, the phase and amplitude functions of PO integrals for a general parametric surface and incident wave are approximated by second order polynomials, first. Although there are some complicated closed-form expressions for these integrals in the literature, the authors present simple and computationally efficient closed-form expressions for them. For this end, the parametric domain of each resulted integral is meshed by triangular boundary-rectangular mesh (TBRM) algorithm. Using this algorithm, the integration domain is divided into some rectangles and triangles. Then, the closed-form expressions are presented for each rectangle and triangle. The closed-form expressions and TBRM algorithm are so fast and accurate that not only the calculation of PO integrals is accelerated but also the relative error of integration is reduced. The relative error of integration can be easily controlled from 10^-2 to 10^-7 or even less. The accuracy and time efficiency of the proposed method are examined by numerical steepest descent path (NSDP) method and brute force integration (BFI) method.