a numerical matching method (NMM) based on the framework of the uniform geometrical theory of diffraction (UTD) is proposed to build the spectral functions for computing the diffraction field by anisotropic impedance wedge at an arbitrary skew incidence. The NMM starts from the coupled integral equations before they are converted into the coupled difference equations as the classic Maliuzhinets methods. Then, the spectral function in the Sommerfeld integral representation of the longitudinal components of the EM field is expanded by a series about the spectrum and the skew incident angle with unknown coefficients. With respect to the oblique incident angle based on normal to the edge incidence or grazing to the edge incidence, the spectral function is derived numerically by solving a system of algebraic equations constructed from the coupled integral equations, after choosing the numerical matching regions on the wedge faces and setting a Sommerfeld numerical integration path. On the basis of the sampled incidences, the asymptotic waveform evaluation (AWE) technique is employed to deduce the spectral function at any other skew incidence in the whole angle space (0°-90°) rapidly. Finally, the UTD solutions are provided far beyond the applicability of the perturbation approach and the numerical examples provide a uniform behavior of the field with respect to the observation angle.
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