广义完全匹配层在二维电磁散射中的应用-电磁场与微波技术专业论文.docxVIP

摘 摘 要 广义完全匹配层在二维电磁散射中的应用 广义完全匹配层在二维电磁散射中的应用 PAGE PAGE III IV IV 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。 关键词：广义完全匹配层；有限差分；吸收边界条件；电磁散射；复扩展变量 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 gene