Numerical study of diffraction and slope-diffraction at anisotropic impedance wedges by the method of parabolic equation: space waves

Abstract

The method of parabolic equation (PE) has been successfully applied to the numerical determination of diffraction, slope-diffraction, and multiple-diffraction coefficients of scalar impedance wedges illuminated by a line source. As a continuation, this paper studies-for the first time to the authors' knowledge-another important canonical problem for the uniform geometrical theory of diffraction (UTD), namely, diffraction and slope-diffraction of an incident cylindrical wave at wedges with anisotropic impedance surfaces, by using the same method. For the diffracted fields, the exact Helmholtz equation is asymptotically approximated by the corresponding parabolic one. It is proved that the sufficient conditions for the unique solution of the Helmholtz equation also guarantee the uniqueness of the solution of the parabolic one. The latter is then efficiently solved by using Crank-Nicholson finite-difference (FD) scheme. Due to the lack of exact solutions, the PE results were compared to uniform asymptotic theory of diffraction (UAT) ones for weak anisotropy and, in this case, very good agreement has been achieved. The diffraction and slope-diffraction behavior dependent upon the measure of the weakness of the anisotropy has been demonstrated by several examples.