电磁散射分析中的谱元抛物线方程方法

发布时间：2018-03-26 16:50

本文选题：抛物线方程方法　切入点：谱元法　出处：《南京邮电大学》2015年硕士论文

【摘要】：电磁场数值计算方法在电磁仿真领域中得到了广泛应用,例如频域有限差分法(FDFD)、矩量法(MOM)和有限元法(FEM)等。这些方法在分析电大尺寸目标的电磁散射问题时,虽然计算精度高,但存在着消耗内存多、对计算机配置要求高等缺点。物理光学等高频方法可快速求解且消耗计算机资源少,但其计算精度却不理想。抛物线方程(Parabolic Equation,PE)是由波动方程近似而来,它可以将三维问题降为一系列的二维问题,沿抛物线轴向方向进行迭代求解,在降低了求解难度和计算内存的同时,仍能保证较高的计算精度。本文对电磁散射分析中的谱元抛物线方程方法进行了研究,主要有以下几方面的内容:首先,详细介绍了抛物线方程方法的基本理论,以及三维矢量抛物线方程方法分析电磁散射问题的基本原理和实施过程。其次,分析研究了标量的谱元抛物线方程方法在电磁散射中的应用。有限差分的抛物线方程方法采用规则网格来离散散射目标,足够细密的剖分网格才能模拟散射体外型,而谱元抛物线方程方法采用非规则网格建模的方法能更好模拟散射体外型,提高计算精度。通过双线性插值的方法获得每个步进面上任意点处的场量。在此基础上,详细推导了谱元抛物线方程的表达式,通过数值算例验证了其正确性。最后,研究了矢量的谱元抛物线方程方法在电磁散射中的应用。我们详细推导了矢量抛物线方程对应的谱元法表达式,详细描述了矢量边界条件的处理以及求解过程,并通过数值算例进行了验证。在网格剖分较粗时,谱元抛物线方程方法比有限差分的抛物线方程方法具有更高的计算精度。对于抛物线方程方法的近轴限制,我们可以利用旋转抛物线方程方法来获得散射目标的全向双站雷达散射截面积(RCS);根据单/双站RCS之间的转换关系,可由散射目标的双站RCS快速插值出一定角度范围内的目标单站RCS,通过算例验证了方法的正确性。
[Abstract]:Numerical calculation methods of electromagnetic field have been widely used in electromagnetic simulation, such as FDFDF, mom and FEMM in frequency domain, etc. These methods have high accuracy in analyzing electromagnetic scattering problem of electrically large size targets, such as finite element method (FEM), finite element method (FEM) and finite element method (FEM). However, there are many disadvantages such as high memory consumption and high demand for computer configuration. High frequency methods such as physical optics can be solved quickly and consume less computer resources, but their calculation accuracy is not ideal. The parabolic equation PE) is derived from the wave equation. It can reduce the three-dimensional problem to a series of two-dimensional problems and iteratively solve the problem along the parabola axis. It reduces the difficulty of solving the problem and computes the memory at the same time. The method of spectral parabola equation in electromagnetic scattering analysis is studied in this paper. The main contents are as follows: firstly, the basic theory of parabola equation method is introduced in detail. The basic principle and implementation process of electromagnetic scattering problem are analyzed by three-dimensional vector parabola equation method. Secondly, The application of spectral parabola equation method of scalar to electromagnetic scattering is analyzed and studied. The finite difference parabola equation method uses regular grids to discretize scattering objects. The spectral element parabola equation method using irregular mesh modeling method can better simulate the external scattering patterns and improve the calculation accuracy. The bilinear interpolation method is used to obtain the field quantities at any point on each step surface. The expression of spectral parabola equation is derived in detail, and its correctness is verified by numerical examples. Finally, The application of spectral parabola equation method of vector in electromagnetic scattering is studied. The expression of spectral element method corresponding to vector parabola equation is derived in detail, and the processing and solving process of vector boundary condition are described in detail. Numerical examples show that the spectral parabola equation method is more accurate than the finite difference parabola equation method when the mesh is coarse. We can use the method of rotating parabola equation to obtain the cross section area of omnidirectional bistatic radar for scattering target, according to the conversion relation between single and one bistatic RCS, The bistatic RCS of the scattered target can be rapidly interpolated from a certain angle range. The correctness of the method is verified by an example.
【学位授予单位】：南京邮电大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TN011

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