Spectral Element Method Based Parabolic Equation For EM Scattering Problems

Computational electromagnetics have been widely used in the electromagnetic simulation for electronic engineering. Rigorous techniques like the method of moments(MOM) or the finite difference frequency domain method(FDFD) work well for electrically small objects. More memory requirements are required when the scatterer is electrically large. Less computer resources are required for approximate methods with low accuracy. The parabolic equation(PE) is an approximation of the wave equation. The calculation is taken to march from plane to plane and can be converted into a series of 2D problems to be solved. Both the memory requirement and the CPU time can be saved by the PE method.This paper investigates the spectral element method baesed parabolic equation for EM scattering problems. The main content is as follows:Firstly, the parabolic equation mothed is introduced in detail, including two-dimension standard parabolic equation, three-dimension standard parabolic equation and vector parabolic equation.Secondly, the scalar spectral element method based PE is introduced and analyzed in detail. The irregular grid modeling is better for approximation of scatterer and can improve the accuracy of calculation when the grid is coarse.Finally, the vector spectral element method based PE is introduced and analyzed in detail. The complete bistatic radar cross section(RCS) of scatterer can be obtained by the rotating PE method. According to the conversion relationship between single station RCS and bistatic station RCS, the single station RCS can be obtained by the fast interpolation of bistatic station RCS. Numerical examples demonstrate the efficiency of the proposed method.