Research On Fast Algorithm For Solving Electromagnetic Wave Propagation Problem With Parabolic Equation Method

Currently, the calculation methods for predicting electromagnetic wave propagation characteristics are varied. Among them, the parabolic equation method can calculate the electromagnetic wave propagation characteristics over irregular topography and complex atmospheric structure conditions. Owning to it was able to accurately solve wave propagation problems in complex electromagnetic environment, the parabolic equation method attracted widespread attention. In this thesis, electromagnetic wave propagation characteristics problem is studied based on parabolic equation method.First of all, the basic theory of parabolic equation method is studied. Starting from Maxwell’s equations, the parabolic equation under the rectangular coordinate system is derived from wave equation. Two kinds of commonly used numerical algorithm for solving parabolic equation has been introduced, including finite difference method and step Fourier method. The initial field and boundary conditions required for the numerical algorithm for solving parabolic equations are described in detail, and the numerical solution of parabolic equations is achieved by programming which based on the corresponding theory.Secondly, the problem of electromagnetic wave propagation over large irregular terrain is studied. The method to processing the boundary of obstacle using terrain masking model is described in detil. The electromagnetic wave propagation characteristics over large irregular terrain is reflected by the calculation results which using the split-step Fourier algorithm for solving the parabolic equation.Thirdly, the variable step split-step Fourier algorithm is proposed. This algorithm mainly improve traditional split-step Fourier algorithm, change the fixed step to variable step. To illustrate the implementation process, this thesis gives two examples of irregular terrain, compare to the traditional split-step Fourier algorithm, one example result shows the variable step length algorithm count reduced by about 55%, the calculation time shortened by about 51%; another example shows he variable step length algorithm count is reduced by about 40%, the calculation time shortened by about 32%.Finally, the impact of tropospheric atmospheric structure on electromagnetic wave propagation problem is studied. The type of atmospheric structure is described in detil, the refractive index and its calculation model, and a method for the parabolic equation method to deal with complex structure of the atmosphere is described. Then this thesis gives two examples including electromagnetic wave propagation with a floating waveguide condition and electromagnetic wave propagation on irregular terrain with a normal atmospheric environment.