The parabolic equation model for the numerical analysis of 3D diffraction at an anisotropic impedance wedge

An exact solution for the scattering by an isotropic impedance wedge illuminated by a plane wave perpendicularly incident on its edge was obtained by Malyuzhinets (1958) by expressing the total field in terms of a Sommerfeld spectral integral. A different approach aimed at analyzing the more general case of skew incidence on an isotropic impedance wedge of arbitrary aperture has been presented by Pelosi, Selleri and Graglia (see IEEE Trans. Antennas Propagat., vol.AP-44, no.2, 1996). With this approach the problem is solved by recognizing that the diffracted field away from the edge satisfies a set of parabolic equations. These equations are numerically solved on an open domain by the Finite Difference (FD) method, taking into account appropriate conditions at any shadow and reflection boundary. The FD numerical solution method proposed is derived for a perfectly conducting wedge. We formulate the problem for a plane wave at oblique incidence on a wedge whose faces have different anisotropic impedance boundary conditions (BCs). We summarize the parabolic approach and preliminary results of the anisotropic wedge problem obtained by application of the FD technique are presented.