【作者】 王辉；

【导师】 吴先良； 黄志祥；

【作者基本信息】 安徽大学 ， 电磁场与微波技术， 2011， 硕士

【摘要】 时域有限差分(FDTD)方法作为解决电磁场问题的几种主要的数值方法之一,在进行电磁仿真的时候在FDTD中需要引入低噪声水平的波源,特别是在仿真弱散射问题时。在实际工程问题的研究中,常常需要用到平面波源,比如我们需要计算一个散射体的雷达散射截面(RCS),如果该散射体远离波源的话,就可以用平面波来近似波源在散射体附近产生的场。Taflove提出的总场散射场分离(TF/SF)技术是一种在FDTD中引入波源的高效技术,它对于在FDTD中引入平面波同样有效。TF/SF的数学原理是在电磁场理论中经常以不同形式出现的场的不连续性原理和等效原理。在一定意义上,该技术在只需要重新设置散射体的情况下就可以解决很多散射问题。如果需要,由FDTD仿真得到的近区散射场可以外推得到散射体的远场散射特性。1D incident field array (IFA)是一种有效的时域方法,它在一维上与FDTD主网格同时仿真,然后利用插值、投影技术得到连接边界周围场点的入射场,通过连接边界条件在总场区引入入射场。遗憾的是,因为插值以及波源一维网格和FDTD主网格色散不匹配的问题,会产生非物理的散射波从而影响实际的散射场。针对二维问题本文提出了一种新的高效的平面波源引入方法：分裂平面波FDTD法(SP-FDTD),该方法基于分裂场思想,从根本上消除了波源一维网格和FDTD主网格之间因为色散、各向异性不一致及插值等带来的误差,使得入射场泄露到散射区的误差水平在-300dB左右。论文通过对FDTD中数值平面波特性的研究,对该方法的可行性做了理论上的证明,并推广到三维FDTD和高阶FDTD算法,同时丰富的数值算例也表明了算法的有效性。具体研究工作包括：●针对传统平面波引入方法的缺陷,文章通过理论分析找出了引起该缺陷的原因,并找到消除误差的方法。●针对二维TMz模型,本文基于分裂场思想提出了SP-FDTD方法,并通过对数值平面波特性的研究,从理论上证明了SP-FDTD方法的可行性,其有效性也通过二维情形下丰富的数值算例得到了证实。●通过FDTD中数值平面波的特性和分裂场思想,本文将SP-FDTD方法推广到三维FDTD和二维高阶算法M24中。数值算例也表明该方法在三维FDTD及M24算法中实现了完美的平面波引入,使得泄露误差水平在-300dB。●+最后论文总结分析了该算法的优势以及存在的问题,并就该技术进一步推广应用到辛算法和ADI-FDTD等方法中做了展望。更多还原

【Abstract】 The finite-difference time-domain (FDTD) method, as one of the main methods of numerically solving electromagnetic problems, requires the introduction a volume source into FDTD computational domain, which should has a very low noise level, especially when observing weak scattering. And many practical problems of interest involve the use of plane wave sources, for example, one often needs to calculate the radar cross-section (RCS) of an object where it is assumed that the source is far away, allowing the use of the plane wave approximation.For efficient simulation of a plane wave, the total-field/scattered-field (TF/SF) formulation as outlined in Taflove is such a well-developed method for introducing volume source into FDTD. The mathematical principle of this formulation is rooted at the field discontinuity equations and the equivalence principle, which in electromagnetic theory often manifests in different forms. In a sense, the formulation can solve many scattering problems only by remodeling the scatter. If required, the resulting scattered fields can also be transformed to investigate their far-field properties. An efficient time-domain technique is an auxiliary 1D incident field array (IFA) which is used to propagate a plane wave source concurrent with the main simulation domain, being used as a lookup table to populate the Huygens’ surface. Unfortunately, depending on the formulation used for this source, errors are introduced as a result of interpolation and numerical dispersion mismatches—or equivalently the grid anisotropy—between the source and the main FDTD grid, as this causes a nonphysical scattered field to corrupt results and reduce the dynamic range.For a 2D problem, we present a new but efficient method for introduction of plane wave source, which based on the split-field:the method of splitting the plane-wave FDTD (SP-FDTD), which fundamentally eliminates the error of interpolation and phase velocity mismatch, achieving a perfect TF/SF separation with leakage error around -300dB. In addition, its feasibility is confirmed by the nature of numerical plane wave in FDTD and the SP-FDTD method can also be extended to 3D FDTD and higher-order FDTD (M24) method.Specific studies include the following:(?) Aimed at the traditional method of introducing plane wave source, its deficiency is presented through theoretical analysis, and we propose the way of eliminating leakage error.(?) For the 2D TMZ model, we present a new but efficient method for introduction of plane wave source, which based on the split-field:the method of splitting the plane-wave FDTD (SP-FDTD). By the research on the nature of the numerical plane wave in FDTD, the feasibility of the method is confirmed in theory, and its effectiveness is also confirmed by numerical examples in 2D.(?) Making using of the nature of the numerical plane wave in FDTD and a split-field formulation, the corresponding SP-FDTD is presented for FDTD problems in 3D and M24 method. According to the numerical examples, there both are perfect total-field/scattered-field separations with leakage error around-300dB.(?) Finally, the paper elaborates the advantages and disadvantages of the SP-FDTD method. The paper also makes a prospect to many aspects such as extending the method to symplectic algorithm, ADI-FDTD and so on.更多还原