任意三维物体FDTD共形网格生成算法

时域有限差分法(FDTD)是计算电磁学广泛使用的方法之一.作为一种数值方法,首先要对目标模型进行网格离散.它直接影响到计算的精确性与复杂性.为了避免采用Yee氏单元对复杂模型建模所产生的阶梯误差,实现了一种任意复杂形状三维物体FDTD共形网格自动生成算法.对于由AutoCAD等建模软件生成的目标模型(三角形和四边形构成),应用计算机图形学方法求出网格线与模型的交点,在三个网格面分别生成共肜网格.数值结果证实了共形网格生成方法的正确性和在提高FDTD方法计算精度方面的有效性.     

共形PML下三维电磁散射矢量有限元计算

共形完全匹配层吸收边界能满足复杂构型散射体的几何外形要求,又具有良好的电磁波吸收特性,大幅度减少了散射区网格的数量,达到节省计算机存储量的目的。在ANSYS采用的六面体矢量单元的基础上,对矢量基函数作了一些增强正交性的修改,使其同时具备采样点正交性和积分正交性,得到了一种新的正交增强六面体矢量单元;这种新单元能增强系统矩阵的对角占优特性,加快系统方程组的求解速度。数值算例表明,在共形完全匹配层条件下,采用新的正交增强矢量单元进行三维电磁散射计算既能减少计算存储量,又能提高计算速度和精度,具有工程应用价值。     

基于CUDA架构的三维CPML-FDTD并行方法

为解决时域有限差分（FDTD）算法应用于电大尺寸目标仿真的巨大耗时问题,应用FDTD算法的并行特性和通用图形处理器（GPGPU）技术,实现了一种基于计算统一设备架构（CUDA）的三维FDTD并行计算方法,采用了时域卷积完全匹配层（CPML）吸收边界条件模拟开域空间,对不同网格数目标仿真计算。进一步结合FDTD算法和CUDA的特点进行了优化,当计算空间元胞数在十万数量级及以上时,优化前后GPU运算相对于同时期的CPU分别可获得10和25倍以上的加速,结果表明该方法较适合用于实际电磁问题的仿真。     

基于三角面元的FDTD网格生成与可视化实现

针对三维复杂目标利用时域有限差分法(FDTD)进行电磁数值计算中遇到的Yee元胞建模的难题,提出了一种将三维三角面元模型转换为Yee元胞模型的方法,方法的实质是判断Yee元胞的中心点是否在目标模型的内部或是表面,根据判断后输出的结果进行了FDTD数值计算,计算结果证明了方法可以正确且快速的实现时域有限差分法的自动网格剖分,实现了FDTD网格的自动剖分.并利用OpenGL技术编程实现了剖分模型的可视化,有效的提高了时域有限差分法的电磁仿真系统预处理的能力.     

FDTD方法吸收边界条件的研究及应用

用时域有限差分法(FDTD)求解电磁散射问题中,吸收边界条件的设置起着关键性作用.通过时间和空间上的递推算法对时域有限差分法中的两种吸收边界条件:Mur吸收边界条件和完全匹配层(PML)的吸收效果进行了比较和分析.同时,引入参数对PML的差分方程进行了优化,避免了将电磁场分裂为两个分量进行计算,进而降低了计算内存开销.实验结果证明PML具有更优越的吸收性能.最后,在FDTD算法中应用PML吸收层对一圆柱形导体的雷达散射截面积(RCS)进行数值仿真,验证了FDTD算法在计算雷达散射截面积(RCS)上的有效性.     

基于OpenCL的GPU加速三维时域有限差分电磁场仿真算法研究

提出了一种基于开放运算语言（OpenCL）的GPU加速三维时域有限差分（FDTD）电磁场仿真计算的方法．该方法利用图形处理单元（GPU）的并行处理特性并结合OpenCL接口标准实现了时域卷积完全匹配层（CPML）吸收边界条件的三维FDTD的高性能加速计算．首先设置FDTD仿真参数并动态申请内存空间,然后初始化OpenCL的计算参数,对三维电磁模型基于OpenCL进行FDTD加速仿真．本方法显著提升了FDTD电磁场仿真速度,与利用CPU计算相比速度提升可达5-8倍,且具有CPML吸收边界条件,可以模拟电磁波在自由空间的传播;基于OpenCL编译的语言程序可以运行在CPU或GPU硬件上,并可充分发挥多核CPU的并行计算能力,使得FDTD电磁场仿真具有更广泛的实际应用．     

基于OpenGL三维非均匀FDTD网格图形的消隐处理*

在分析了三维非均匀FDTD网格图形性质及计算数据结构特点的基础上,提出了一种基于OpenGL深度缓冲机制的绘图方法,采用多边形深度偏移量修正法进行精细化的消隐修正,实现了网格图形的快速生成与高效消隐,大大提高了FDTD仿真及模拟计算网格图形的可视化效果,并在此基础上设计并实现了基于OpenGL的三维网格模型仿真系统.最后,以U型天线的网格图形为例,展示其可视性.     

超宽带信号地面回波仿真方法研究

研究地面的超宽带回波特性,能够为超宽带无线电系统设计提供仿真支持。为保证计算结果的可信性,需要考虑土壤的色散特性和地面起伏对回波的影响。目前在超宽带地面回波计算中所使用的FDTD（时域有限差分）算法计算量较大或者存在较大误差。使用卷积完全匹配层（CPML）作为吸收边界,多极点Debye模型描述土壤介质特性,在FDTD算法基础上推导出了多极点Debye介质的CPML-FDTD算法。对不同条件地面的回波进行了仿真计算,与未使用PML（完全匹配层）的FDTD算法计算结果进行比较分析,表明文中使用的算法结果正确且效率较高。     

修正共形FDTD技术在声散射中的应用

传统时域有限差分法(UFDTD)将曲面目标边界作为台阶近似来处理,当网格划分不很精细时,计算结果会有很大的误差.共形技术可以解决这一问题,但它要满足一定的共形条件,实现起来比较困难.针对刚性目标的声散射问题,提出一种修正共形技术,它不需要满足任何共形条件就能达到很好的稳定性.文中给出了此共形技术的基本原理和稳定性证明,并针对声散射问题进行数值模拟.仿真结果表明:在同样计算量的情况下,此方法的计算精度明显高于传统方法;在同样计算精度的情况下,此方法的计算量大约比传统方法节省50%.     

全波场地震波数值模拟中的边界处理实践研究

在用有限差分法或有限元法模拟无界区域中的波动时,需要对计算区域的边界做特殊处理,以消除由于把地震波的传播设定在有限区域而产生的边界反射。为了这一目的,人们研究出了多种人工边界处理方法,完全匹配层（PML）吸收边界条件就是理想的方法之一,现已被广泛应用。本文将PML吸收边界条件应用于全波场地震波的数值模拟,数值计算实验表明,对qP波,匹配层的厚度为5个网格间距即可达到要求,而对qSV波与qSH波,为达到理想的吸收效果,匹配层的厚度应当增大,当厚度为13个网格间距时达到了理想的吸收效果。     

Rigorous interference and diffraction analysis of diffractive optic elements using the finite-difference time-domain method

The Finite-Difference Time-Domain (FDTD) method has proven to be a useful tool to analyze electromagnetic scattering phenomena. In this work, the FDTD method is applied at optical wavelengths. More precisely, we present the results obtained using the FDTD algorithm to simulate the performance of optical devices such as volume diffraction gratings. The Perfectly Matched Layers (PML), Total-Field Scattered-Field formulation (TF/SF) and Near-Field to Far-Field transformation (NF/FF) are some add-ons included in order to correctly calculate the far field distribution obtained from the numerical near-field values computed in the simulation region. These values in the near-field region are computed by illuminating the grating with of a plane wave at the Bragg angle of incidence. In addition, we compare the results obtained by the FDTD method to those obtained using the Rigorous Coupled Wave Theory (RCWT) applied to diffraction gratings. As will be seen in this paper there is good agreement between the two approaches, thus validating our FDTD implementation.     

基于FDTD的机载短波天线辐射特性分析

机载天线辐射特性的研究对于机载天线的设计与布局具有重要的意义。机载天线在机身的影响下会改变其原有辐射特性,针对上述问题采用时域有限差分法(FDTD)对机载短波天线的辐射特性进行了分析,并应用FDTD对某型号机载短波天线进行了仿真:使用软件建立整机模型,应用自适应网格对其进行了剖分,设置了PML吸收边界,添加激励并计算得出增益方向图,最后将仿真结果与实测结果进行了比较,二者在天线工作频带内吻合,验证了FDTD对机载天线辐射特性进行分析的有效性与实用性。     

A finite‐difference time‐domain approach to waveguide discontinuities using one‐dimensional modal perfectly matched layer based on diagonally anisotropic material

In this paper, one‐dimensional modal perfectly matched layer (PML) is applied to improve the computational efficiency in waveguide discontinuity problems. The proposed PML formulation is based on an anisotropic medium. A WG‐90 rectangular waveguide with a thick asymmetric iris is analyzed via FDTD simulations with Berenger's PML and the proposed one. Numerical results show that the computational efficiency is significantly improved by the new method. © 2000 John Wiley & Sons, Inc. Int J RF and Microwave CAE 10: 264–270, 2000     

Bandpass signal formulation with hybrid implicit-explicit procedure in open regions for unmagnetized plasma

The finite-difference time-domain (FDTD) algorithm shows disadvantages in bandpass signal simulation with fine structures along a single direction. The reason is that FDTD algorithm exists the Courant–Friedrichs–Levy (CFL) condition and bases on the lowpass-sampling theorem. Based on the numerical implementation, hybrid implicit-explicit procedure and complex envelope method are introduced. As a full-wave simulation method, higher order concept is incorporated into perfectly matched layer (PML) formulation for improving absorption at boundaries of the lattice. For unmagnetized plasma simulation, piecewise linear recursive convolution method is modified according to the bandpass signal. Through numerical example, the proposed algorithm shows considerable performance during the entire simulation which can be concluded from several aspects: (1) It takes advantages of higher order concept which shows enhanced absorption. (2) The proposed algorithm can overcome the CFL condition and maintain stability with the increment of time steps. (3) It shows considerable efficiency and accuracy in simulating structures with fine details along a single direction. (4) It can alleviate time increment problem among implicit algorithms with lower CFL numbers.     

单极天线的计算机仿真设计

aa输入阻抗,在PML边界条件采用指数差分的形式,减少了误差,与文献比较,获得比较好的结果。     

基于卷积的Perfect-Match-Layers吸收层算法及其在PIC程序中的应用

基于卷积的PML吸收层算法能够吸收各种频率、各种传播方向、各种传播速度的电磁波,同时具有计算量小、吸收率高、可并行性好等突出特点。改进基于卷积的PML算法的差分形式,使之适合于PIC粒子模拟,编制了相应代码。对该算法的测试表明,对各种角度的散射电磁波振幅的吸收率达到0.999以上。     

蝶形天线的计算机仿真设计

蝶形天线是在脉冲型探地雷达中广泛采用的一种宽带天线。本文采用时域有限差分算法(FDTD)结合PML吸收边界条件分析了蝶形天线在高斯脉冲激励下的时域特性,通过傅立叶变换,计算出天线的方向图和在不同频率下的输入阻抗,结果表明FDTD算法用于分析蝶形天线是有效的。     

用于时域有限差分计算的通用C++类库

设计了时域有限差分法相关C 类库,在其基础上编制了高斯光束的时域有限差分计算程序,所得数值计算结果与精确解进行了比较,二者吻合良好。该类库可用于进行确定性电磁场问题的时域有限差分仿真,类库结构清晰、代码重利用率高、易于维护和扩充。     

Perfectly matched layers for time-harmonic elastodynamics of unbounded domains: theory and finite-element implementation

One approach to the numerical solution of a wave equation on an unbounded domain uses a bounded domain surrounded by an absorbing boundary or layer that absorbs waves propagating outwards from the bounded domain. A perfectly matched layer (PML) is an unphysical absorbing layer model for linear wave equations that absorbs, almost perfectly, outgoing waves of all non-tangential angles-of-incidence and of all non-zero frequencies. This paper develops the PML concept for time-harmonic elastodynamics in Cartesian coordinates, utilising insights obtained with electromagnetics PMLs, and presents a novel displacement-based, symmetric finite-element implementation of the PML for time-harmonic plane-strain or three-dimensional motion. The PML concept is illustrated through the example of a one-dimensional rod on elastic foundation and through the anti-plane motion of a two-dimensional continuum. The concept is explored in detail through analytical and numerical results from a PML model of the semi-infinite rod on elastic foundation, and through numerical results for the anti-plane motion of a semi-infinite layer on a rigid base. Numerical results are presented for the classical soil–structure interaction problems of a rigid strip-footing on a (i) half-plane, (ii) layer on a half-plane, and (iii) layer on a rigid base. The analytical and numerical results obtained for these canonical problems demonstrate the high accuracy achievable by PML models even with small bounded domains.