积分方程快速傅里叶变换方法在电磁散射问题中的应用

摘要随着计算机与电磁学的飞速发展，电磁特性分析在天线设计，电路设计以及隐身与反隐身等方面起着越来越重要的作用。由于传统的基函数（如 RWG 基函数）要求剖分单元共形，这使得电磁建模的难度大大增加。本文使用的一种基于格点稳定的高阶矢量基函数和一种非共形体积分方法，可以处理非共形的面剖分单元和体剖分单元，这对于某些精细结构的电磁建模是很有意义的。为了加速计算，本文采用了积分方程快速傅里叶变换（ Integral Equation Fast Fourier Transformation，简称 IE-FFT）与基于格点稳定的高阶矢量基函数相结合的方法来加速迭代求解过程中的矩矢相乘。5561
本论文首先从积分方程出发，介绍了表面积分方程和体积分方程方法，并研究了用矩量法（Method of Moments，简称 MoM）来求解积分方程的具体过程。
其次，研究了积分方程快速傅里叶变换方法。详细介绍了其原理及具体实现
的过程。
再次，介绍了基于格点稳定的高阶矢量基函数及其积分方程方法数值实现，并将基于格点稳定的高阶矢量基函数与积分方程快速傅里叶变换方法相结合来加速电磁计算。
最后，介绍了处理介质问题的一种非共形体积分方法，研究了如何运用这种非共形体基函数来求解体积分方程，并且将这种非共形体基函数与积分方程快速傅里叶变换方法相结合来加速介质体电磁计算。进一步地，研究了复合金属介质结构的完全非共形方法，结合积分方程快速傅里叶变换方法计算了典型结构的电
磁特性。
关键词矩量法，积分方程，积分方程快速傅里叶变换，格林函数
毕业设计论文外文摘要
Title A NOVEL GAUSSIAN INTERPOLATION FORMULA-BASED IE-FFT ALGORITHM FOR SOLVING EM SCATTERING PROBLEMS
Abstract With the rapid development of computer and electromagnetics, electromagnetic analysis is more and more important in antenna design, electrical circuit design and stealth and anti-stealth technology etc. Since the traditional basis functions （such as RWG basis functions） need conformal mesh, electromagnetic modeling is very difficult. This thesis uses a kind of grid-robust higher order vector basis functions, and a kind of nonconformal volume integral equation， which can deal with nonconformal mesh of surface and volume. This is very significant for the electromagnetic modeling of complicated structure with very fine meshes. To accelerate the computation, the integral equation-fast Fourier transformation （ IE-FFT ） is combined with the grid-robust higher order vector basis functions in this thesis to speed up the matrix-vector multiplication in the iteration.
At first, integral equation is introduced in detail, including surface integral equation and volume integral equation. The method of solving integral equation with the method of moment （MoM） is also studied.
Secondly, the integral equation-fast Fourier transformation is studied. The theory and implementation of the integral equation-fast Fourier transformation method are introduced in detail.
Thirdly, the grid-robust higher order vector basis functions and the realization in integral equation are introduced. The grid-robust higher order vector basis functions combined with integral equation-fast Fourier transformation are used to speed up the computation.
At last, a kind of nonconformal volume integral equation used to deal with dielectric object is introduced. The process of solving volume integral equation with this kind of nonconformal volume basis function is studied. The combination of nonconformal volume integral equation and the integral equation-fast Fourier transformation is used to accelerate the computation. Farther more, the nonconformal mesh of the composite penetrable structure and PEC is studied, and the electromagnetic property of typical structure is analyzed by integral equation-fast Fourier transformation method. 积分方程快速傅里叶变换方法在电磁散射问题中的应用:http://www.751com.cn/shuxue/lunwen_2631.html