一种新时域交替隐式差分算法在散射问题中的应用

提出一种新时域交替隐式有限差分(ADI-FDTD)算法格式. 传统ADI-FDTD算法的 场量步进方程涉及周围若干网格的较多场量，导致两个区域的步进方程处理较困难：一个是 邻近完全匹配层(PML)和散射场交界区，另一个是邻近连接边界区. 特别是后者，考虑入射 波影响需对场量所在区域判断，根据不同情况对原有方程进行修正，一维和二维散射问题 相对简单，可三维问题修正式有数十种之多而几乎无法完成. 本方法基于分裂场形式的ADI- FDTD技术，使得散射场区和PML吸收层区的表达形式完全一致，从而忽略两者差别.另关键词：时域交替隐式有限差分算法电磁散射

A new ADI-FDTD analysis in electromagnetic scattering

This paper proposes a new set of alternative direction implicit finite-difference time-domain (ADI-FDTD) equations. In conventional ADI-FDTD,the update equation is related to several field components in cells nearby,which will lead to some difficulties in two regions:1) around the boundary region between the perfectly matched layer (PML) and the scattering field; 2) around the adjacent boundary. Especially,in the region around the adjacent boundary,owing to the incident wave,we should make a judgment about the situation of every component and modify the update equation. It is potential to make a solution to one-dimensional or two-dimensional problem. However,in three-dimensional (3D) analysis,one equation concerns with eleven components and there exist several tens of cases to be modified. This makes the scheme very tedious and impossible to realize. This paper adopts the split field difference formation in the whole computation regime to analyse the scattering problem. Because the equations in the scattering field region have the same expressions as those in PML absorber except for some coefficients,the boundary in the region mentioned above can be ignored. Due to simplicity of the split field equation,the new ADI-FDTD formula in 3D problem has only five components to be considered and four modifications at the adjacent boundary to be made. Finally,we utilize this new method to compute some electromagnetic scattering numerical examples,and the results are in excellent agreement with those obtained with other algorithm and the measured data. Moreover,the new method have 6-7 times higher efficiency in terms of the CPU time.