The Research On Electromagnetic Scattering And Propagation Based On The Parabolic Equation Algorithm

The Parabolic Equation method (PE) is an approximation of the wave equation, which models energy propagating in a cone centred on a preferred direction, the paraxial direction. The parabolic approximation was introduced to treat the problems of propagation of sound wave and optics. In recent years, it was realized that PE method may also be adopted as a numerical method of electromagnetic field calculation, bridging the gap between rigorous methods like the method of moments(MOM) or Finite Difference Time Domain(FDTD), which solve Maxwell's equations exactly, and asymptotical methods based on ray-tracing or physical optics. Using PE method can avoid the problems of the limitation of CPU time and memory required by these rigorous methods. It can also reduce the error caused by the high-frequency approximation.This thesis mainly focuses on the PE algorithms applied to the computation of electromagnetic scattering and propagation problems. The main works are listed as follows:1. The Parabolic Equation algorithms were deduced rigorously, including two-dimensional standard parabolic equation, two-dimensional(2-D) backward standard parabolic equation, three-dimensional(3-D) standard parabolic equation and vector parabolic equation. Based on standard parabolic equation, the expansion of pseudo-differential operator is improved by the least square approximation. The accuracy was further improved.2. The 2-D and 3-D absorbing boundary conditions (Perfectly Matched Layer (PML) based on complex coordinate stretching) were analyzed and deduced specifically. They were not only applied to the analysis of electromagnetic scattering, but also employed to implement electromagnetic wave propagation problems in unbounded space.3. The PE algorithms were used to compute the monostatic and bistatic Radar Cross Section(RCS) of some standard scatterer with the rotating PE method, including the backscattering RCS, multiple scattering and 3-D scatterer's RCS.4. Radio wave propagation over the irregular terrain was emulated accurately...