The closed-form frequency-independent solution for physical optics integrals on conducting quadratic surfaces using rectangular meshing

In this paper, we propose a closed-form frequency-independent solution for highly oscillatory Physical Optics (PO) integrals on a quadratic surface. These integrals are highly oscillatory integrals with second order polynomial phase and amplitude functions. First, using an affine transform, the quadratic complete form of the phase function is converted into a simple canonical form. Then, the resulted integration domain is divided to some rectangles. Finally, the closed-form solution is represented on each rectangle. Actually, by adjusting the integrand and the integration domain, we could use the closed-form solution. The accuracy and computation time efficiency of proposed method are studied using some numerical examples.