An Efficient Method to Compute Fock Integrals for High-Frequency Electromagnetic Scattering From Coated Convex Surfaces by Numerical Contour Deformation

The uniform theory of diffraction (UTD) method is used to compute the scattered field from electrically large convex scatterers. In this work, a new steepest deforming path (SDP) is proposed to calculate coated Fock-type integrals in the UTD framework more efficiently. The traditional deforming path (DP) leads to exponential and rapid oscillations of the Fock-type integrand in the lit region as frequency increases, leading to computational inefficiencies. Therefore, the SDP method valid in the lit region is presented to reduce these oscillations and induce rapid attenuation of the integrand, significantly improving the computational efficiency of the integral. Furthermore, an adaptive quadrature scheme is presented to enhance calculation speed. Numerical examples verify the precision of Fock-type integral results computed with the proposed SDP. When the electrical size <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ka</i> exceeds 200, the CPU time for computing the coated scattered field from convex scatterers by the SDP method is 25 times faster than that by the DP method. The error between the analytical solution and the SDP method is less than 0.2 dB.