High frequency electromagnetic (EM) scattering analysis from the electrically large scatterers is important to the computational electromagnetics community. Meanwhile, the high frequency diffraction technique, like the uniform geometrical theory of diffraction (UTD), is very important when the observation point lies in the transition, shadow and deep shadow regions of the considered scatterer. Furthermore, the diffracted fields arising from the electrically large scatterers via the UTD technique are usually highly oscillatory in nature, which is named as the Fock type integrals with the Airy function and its derivative involved. In this work, we propose a Fourier quadrature method to calculate the Pekeris integrals. Moreover, we first adopt the Fourier quadrature technique to calculate the diffracted fields from the dielectric convex cylinder with impedance boundary conditions, like the creeping wave fields and NU-diffracted wave fields. On invoking the Fourier quadrature method, the results of total scattered fields at the fixed observation points could achieve 1 dB relative errors. Moreover, numerical results demonstrate that the computational efforts for the oscillatory Pekeris-integrals are independent of wave frequency with the fixed sampling density and integration limit.
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