Two-Way Propagation Modeling of Expressway With Vehicles by Using the 3-D ADI-PE Method

The two-way (2W), 3-D parabolic equation (PE) is first derived and solved by the finite differential (FD) method of alternating direction implicit (ADI) scheme in this communication. By using the 2W PE, both the forward and backward propagating effects can be taken into consideration. Moreover, the calculation can be taken in a marching manner by applying the FD method along the paraxial direction, and the unknowns are computed line by line in each transverse plane. In this way, the computational resources can be saved significantly. The proposed 2W 3-D ADI-PE method is used to analyze the electromagnetic propagating in the expressway with vehicles. The vehicles can be modeled with high accuracy by using the finite-difference scheme. Moreover, the proper impedance boundary conditions are added to the road of expressway and vehicles are regarded as the perfectly electrical conducting targets. Numerical results are given to demonstrate the electromagnetic propagation of expressway with vehicles.