基于地震波正演模拟的边界算法研究

地震波正演模拟存在边界反射,构建人工边界吸收条件是消除边界反射的核心部分。针对传统边界吸收条件受入射角度影响,造成边界反射吸收不够彻底,对边界反射提出优化的PML吸收边界条件,能够克服入射角导致的吸收不完全的问题。首先,将模型区域划分为计算域和匹配层两部分;其次通过波动方程做坐标变化且加入衰减函数,经过傅里叶变化得到PML边界的声波方程;最后,当由计算域过渡至匹配层时,匹配层采用优化后衰减因子,从而达到消除边界反射的目的。通过对边界吸收算法研究表明,优化后PML(perfectlymatched layer,PML)吸收边界条件能够对边界反射获得更好的正演模拟结果,对不同入射角能做到完全吸收的效果。     

两种适用于时域有限体积方法的截断边界

将广泛用于时域有限差分(FDTD)的各向异性完全匹配层推广到非结构网格下格子中心型时域有限体积方法(UCFVTD)中,并同Silver-M(u)ller截断边界相结合,提出了一种适用于UCFVTD的截断边界条件.将良态完全匹配层推广到三维UCFVTD计算,给出了三维情况下UCFVTD算法在良态完全匹配层中的场方程.通过数值反射试验以及对典型的电磁场散射问题的计算,验证了这两种截断边界条件的有效性和整体算法的稳定性.同以往的Silver-M(u)ller吸收边界比较,反射误差分别有15～25 dB和17～28 dB改善,提高了计算精度.     

基于自适应遗传算法的FDTD中完全匹配层的设置方法

针对时域有限差分算法进行电磁场数值求解时的PML吸收边界层的设置问题,给出了利用自适应遗传算法对吸收层的电导率进行优化确定吸收层电导率的方法,得到了相同激励源下吸收效果最佳的吸收层各层电导率值,该值只是经典边界电导率取值的边界反射场值的1/5不到,而且随着计算时间的增长,吸收稳定性增强,可以更加准确地进行电磁场数值模拟。     

截断各向异性介质的修正NPML吸收边界条件

基于各向异性介质中的时域有限差分（Finite-Difference Time-Domain,FDTD）方法及近似完全匹配层（Nearly Perfect Match Layer,NPML）原理,提出一种截断各向异性介质的修正的NPML吸收边界条件.通过对Maxwell旋度方程中的空间偏导数进行坐标拉伸并结合空间插值方法,推导出易于在FDTD方法中实现的吸收边界公式.计算了电偶极子辐射场的反射误差,验证了这种吸收边界截断二维各向异性介质的有效性.三维算例中数值模拟了时谐场的相位分布,以及不同网格NPML吸收层随时间变化的反射误差.数值结果表明NPML吸收边界能有效吸收各向异性介质中的电磁波.     

采用PML的FDTD方法对矩形微带天线的研究

将完全匹配层(PML)吸收边界应用于微带结构中，对矩形微带天线进行了分析计算，给出了其时域和频域的仿真结果。结果表明，与传统的Mur边界相比，采用PML吸收边界具有反射小、馈源模型简单、收敛速度快等优点。     

数值分析渐变DBR对垂直腔面发射激光器谐振腔模的影响

通过数值分析研究了含线性渐变层的Al0.9Ga0.1As/AlyGa1-yAs/GaAs/AlxGa1-xAS DBR的光学特性及其对VCSEL谐振腔光学特性的影响,建立了渐变型DBR渐变层厚度与折射率的关系,通过特征矩阵法计算了突变GaAs/Al0.9Ga0.1AS DBR和渐变型DBR的反射谱和反射相移,分析了渐变层对DBR反射率和反射相移的影响.对渐变型DBR,要使VCSEL谐振腔满足中心波长相位匹配条件,还需要在DBR靠近谐振腔一侧的最前面增加一定厚度的渐变层,称为相位匹配层.通过计算,我们得到了使VCSEL谐振腔满足相位匹配条件时均匀层和相位匹配层的厚度.     

数值分析渐变DBR对垂直腔面发射激光器谐振腔模的影响

通过数值分析研究了含线性渐变层的Al0.9Ga0.1As/AlyGa1-yAs/GaAs/AlxGa1-xAS DBR的光学特性及其对VCSEL谐振腔光学特性的影响,建立了渐变型DBR渐变层厚度与折射率的关系,通过特征矩阵法计算了突变GaAs/Al0.9Ga0.1AS DBR和渐变型DBR的反射谱和反射相移,分析了渐变层对DBR反射率和反射相移的影响.对渐变型DBR,要使VCSEL谐振腔满足中心波长相位匹配条件,还需要在DBR靠近谐振腔一侧的最前面增加一定厚度的渐变层,称为相位匹配层.通过计算,我们得到了使VCSEL谐振腔满足相位匹配条件时均匀层和相位匹配层的厚度.     

色散媒质中的完全匹配层吸收边界

将Ａ．Ｐ．Ｚｈａｏ提出的与媒质无关的完全匹配层吸收边界推广到色散媒质中,推导出了用于色散媒质的无反射完全匹配条件。并对导电媒质进行了数值实验,结果十分理想。与Ｑ．Ｈ．Ｌｉｕ的方法相比,该方法可以应用到更复杂的媒质中。而与Ｓ．Ｄ．Ｇｅｄｎｅｙ的各向异性媒质吸收层相比,在角区的处理要简单得多,更适合于时域有限差分法,对于三维问题更是如此。     

带ABC底面的共形完全匹配层按层积分算法

本文构造了一种共形完全匹配层(Conformal Perfectly latched Layer,CPML)矢量单元按层积分算法,将多层单元积分运算叠加到一层单元中进行,即保留了多层单元的几何和材料信息,又减少了计算规模;为了进一步增强吸收,减少底面反射,应用矢量ABE(Absorbing Boundary Condition,ABC)吸收边界作为CPML底面.数值算例表明,这种按层积分CPML结合矢量ABC吸收边界的方法,吸收效果好,计算量小,效率高;具有良好的应用前景.     

基于有效导热系数法的交界面形状识别算法

基于表面测温的边界形状识别算法研究是红外无损检测技术从定性到定量发展的理论基础,同时也是传热反问题研究的一个重点也是难点问题。对于交界面形状的识别,常规的边界识别算法,由于交界面要在迭代过程中不断变化,所以计算相对复杂,不利于算法的实际应用。在原有边界形状识别研究工作的基础上,通过将交界面形状的识别问题转化为有效导热系数的分布问题,将计算温度和检测温度的吻合程度作为判别条件,利用改进的一维修正算法反演识别有效导热系数的分布,再转化为真实的交界面形状。数值实验表明该方法大大降低了交界面形状识别的复杂性,是解决交界面形状识别问题的行之有效的计算方法。     

Accurate Physical Modeling of Discretization Error in 1-D Perfectly Matched Layers Using Finite-Difference Time-Domain Method

In this paper we present an accurate physical model of discretization error in a 1-D perfectly matched layer (PML) using the finite-difference time-domain method. The model is based on the concept of the discrete wave impedance of the PML. This concept implies that the wave impedance in the discretized space changes, with respect to the continuous value, when absorption occurs. These changes depend on the absorption per unit length, as well as on the discretization step. In the discretized space, both, the magnitude and phase of wave impedance are modified. We employ numerical simulations obtained using a 1-D code to test the proposed model. We then compare the results with those obtained from coaxial wave guide geometry using a commercial 3-D software package. One important consequence of this modeling scheme is the feasibility of the PML without return losses due to discretization error. In practice, numerical results show that by correctly adjusting the electromagnetic parameters of the PML (electric permittivity and magnetic permeability), a significant improvement in the reflection characteristics is obtained. In some cases, it could be as much as 78 dB. The remaining return losses are successfully explained as second-order effects related to the discontinuity of electromagnetic parameters at the interface between the simulation space and PML.      

脉冲波反射折射特性的分析计算

利用FDTD法和PML技术计算分析了平面分界面对脉冲波的反射和折射,充分而形象地描绘平面界面对脉冲波反射的时域过程。通过对折射波的分析获得下述结论：当入射角小于临界角时,折射波波前与几何光学原理一致,当入射角大于临界角时,沿界面传播的折射波不是慢波,而是以媒质Ⅱ的速度传播。所得结果有助于加深对脉冲波反射和折射性质的理解。     

PML吸收边界的时域有限差分法的数值色散研究

PML吸收边界以其优异的吸收能力与效果而倍受人们的关注。本文针对运用PML吸收边界的时域有限差分法的数值色散问题进行了研究,并得到了较为满意的结果,PML吸收边界在有效减少电磁 波在边界上的反射的情况下,并没有带来对数值色 散的不良影响。     

一种新的简化行波边界条件在FDTD算法中的实现

本文提出一种新的边界条件。这种边界条件在边界处强加理想导体对计算场区进行截断,而将由此产生的反射场分离去除,从而减小反射所产生的干扰。与PML边界条件相比,由于它不需要吸收层,不需要PML层中人为的场量分解,因此节约了内存,提高了计算速度。文中给出一维、二维空间的计算实例,计算结果表明原理是可行的。     

The design of Maxwellian absorbers for numerical boundaryconditions and for practical applications using engineered artificialmaterials

A Maxwellian material interpretation of the Berenger (see J. Computat. Phys., vol.114, p.185-200, 1994) perfectly matched layer (PML) is developed using polarization and magnetization fields. The PML material is found to be a passive lossy electric and magnetic medium with particular conductivity and Debye dispersion characteristics. Although it is recognized that the PML medium is physically unrealizable, this polarization and magnetization field interpretation reveals the necessary characteristics of a perfect electromagnetic absorber. A Maxwellian material that has perfect absorption properties and may be physically realizable is derived with these concepts. This Maxwellian absorber is based upon a time-derivative Lorentz material (TD-LM) model for the dispersive and absorptive electric and magnetic properties of a material. This TD-LM model represents a straightforward generalization of the standard Lorentz material model to include the time derivatives of the fields as driving mechanisms for the polarization and magnetization fields. The numerical implementation of the perfect absorber is given and the resulting reflection coefficients from a perfect electric conductor-backed slab of this material are characterized. It is shown for broad bandwidth pulsed fields that this Maxwellian TD-LM slab, like the non-Maxwellian PML, has absorption characteristics in the 70-110-dB range for large angles of incidence. Strategies are discussed for engineering this dispersive electric and magnetic TD-LM absorber artificially with a substrate that has an array of pairs of appropriately designed small coil-loaded dipole radiating elements embedded in it     

Enhanced PML performance using higher order approximation

In this paper, the perfectly matched layer (PML) based on transformation of space into the complex domain is assessed in the method-of-lines framework. The method used in the assessment is based on field symmetry and has the advantage of eliminating numerical error due to discretization of space. The remaining error, which is due only to reflection from the PML, is used to quantify the PML performance. This assessment method is used to demonstrate that higher order approximation to the transverse second derivative operator results in substantial reduction in the unwanted numerical reflection from the PML, leading to enhanced PML efficiency. By using higher order approximation in tandem with a suitably graded PML loss profile, it is possible to obtain a very efficient PML implementation, making it possible to effectively absorb a beam with a large angular spread using only a few number of sample points in the PML.     

A PML using a convolutional curl operator and a numerical reflection coefficient for general linear media

A general time domain representation of the Chew and Weedon [1994] stretched coordinate perfectly matched layer (PML) absorbing boundary condition is described. This new approach mathematically operates on the spatial field derivatives and allows the PML update equations to be trivially derived from any set of general linear medium update equations. A method for calculating the frequency dependent reflection coefficient for this form of the PML is derived for general linear media. Two and three dimensional numerical test results, which validate the calculation of the reflection coefficient, are presented. The range of numerical tests include the PML matching of free space, a magnetoplasma, and a free space waveguide. Improving the reflection coefficient is examined.     

Improvement to the PML boundary condition in the FEM using meshcompression

Numerical errors encountered when using the perfectly matched layer (PML) absorbing boundary condition with the finite-element method are investigated to discover more efficient implementation schemes. Closed-form expressions for the numerical reflection at an interface between two general biaxial materials are applied to the special case of a PML boundary. Expressions for an anisotropically compressed mesh are then derived, revealing that reflections can be greatly reduced through increasing mesh density only where it is required. Significant improvements over previously reported PML boundaries are demonstrated     

Making use of the PML absorbing boundary condition in coupling and scattering FDTD computer codes

This paper deals with the optimization of the PML absorbing boundary condition in finite-difference time-domain computer codes designed for the solution of scattering and coupling problems encountered in the field of electromagnetic compatibility. The critical parameters of the perfectly matched layer (PML) are estimated in function of the problem to be solved, and a blackbox PML concept is introduced. The blackbox PML renders use of computer codes easy, reliable, and optimum in terms of PML thickness. This is illustrated by various numerical experiments.