The time domain (TD) solution for multiple wedge diffraction case considering plane wave incidence is investigated. The proposed TD solution is based on the representation of the inverse Laplace transform of the corresponding frequency domain (FD) solution in closed form, as it is given by a hybrid of the uniform theory of diffraction (UTD)-physic optics (PO) solution.An algorithm to predict the TD diffracted field after an arbitrary number of perfectly conducting wedges having different interior angles is presented. The algorithm has the major advantage of saving the computation time over the existing formulation when the number of wedges is very large. The source is assumed to be above, bellow, or level with the wedge height. The proposed TD solution is validated with the numerical inverse fast Fourier transform of the FD solution.

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In this paper, the wide-angle two-way parabolic Equation (PE) method is presented and applied for predicting both forward and backward electromagnetic waves propagation in urban environments. The buildings are assumed to be knife-edges or rectangular blocks with vertical sides and flat rooftops, and the terrain is assumed to be flat. The wide-angle Fourier splitstep algorithm is iteratively implemented in a forwardbackward manner to incorporate both forward and backward waves into the solution when there exists obstacles in the propagation environments. Numerical results of the two-way wide-angle PE method are compared with those of the two-way narrow-angle PE method and the one-way PE method for the urban scenario problems.

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