【作者】 刘全刚；

【导师】 宋开宏；

【作者基本信息】 安徽大学 ， 电磁场与微波技术， 2010， 硕士

【摘要】 电磁散射数值分析一般分为微分方程法和积分方程法。微分方程法又分为频域和时域微分方程法,频域微分法主要是有限元法(FEM)和频域有限差分法(FDFD),时域微分法主要是时域有限差分法(FDTD),本文是采用频域有限差分法结合完全匹配层吸收边界条件来解决电磁散射问题。首先介绍了有限差分法的基本原理,以及它的差分格式和离散化,然后详细说明了利用有限差分法解决电磁散射问题的一般步骤,介绍了应用超松弛迭代法和共轭梯度法求解差分方程组的过程,并给出了具体的数值算例。利用有限差分法求解电磁散射问题的关键之一是吸收边界问题,其次具体介绍了完全匹配层(GPML)吸收边界条件的基本原理和公式,并且对广义完全匹配层的性能做了具体的分析。最后研究了广义完全匹配层在金属圆柱、金属方柱中的应用,证明了广义完全匹配层吸收边界对任意极化、任意频率、任意入射角的电磁波可以实现无反射吸收。本文给出了在直角坐标和柱坐标系下广义完全匹配层的优化参数,GPML吸收边界可紧靠散射体去截断差分网格从而能够获得比较精确的数值结果,并对复空间变量参数进行了详细的分析,得出一定的规律。更多还原

【Abstract】 Electromagnetic scattering numerical analysis generally contains differential equation method and integral equation method. Differential equation method is divided into frequency domain differential equation and time domain differential equation. Frequency domain differential method mainly includes the finite element method (FEM) and frequency domain finite difference method (FDFD). Time domain differential method mainly includes the finite difference time domain method (FDTD). This paper used frequency domain finite difference method in conjunction with perfectly matched layer absorbing boundary conditions to solve electromagnetic scattering problems.Firstly, the basic principles, difference format and the discretization of finite difference method is introduced, then basic process for analyzing electromagnetic scattering problems using finite difference methods and the course for calculating differential equations using SOR and conjugate gradient method are introduced and then several numerical examples are calculated.One key point of analyzing electromagnetic scattering problems using finite difference method is absorbing boundary condition. Secondly, the basic principles and formulas of generalized perfectly matched layer (GPML) absorbing boundary conditions are introduced, and the capability of generalized perfectly matched layer is analyzed.Finally, applying generalized perfectly matched layer in the metal cylinder and metal square columns is studied, which proved that the generalized perfectly matched layer absorbing boundary can absorb electromagnetic waves of any polarization and any frequency and incident angle Unconditionally In this thesis, the optimization parameters of generalized perfectly matched layer in rectangular coordinates and cylindrical coordinates are given, GPML absorbing boundary can be close to the truncated differential scattering grid in order to obtain accurate numerical results.The parameters of complex space variables are analyzed detailedly and the characteristics are obtained.更多还原