电磁脉冲作用下地面铺设屏蔽电缆蒙皮电流分布的时域计算方法研究

为克服传输线理论方法求解电磁脉冲电缆耦合问题存在的不足，对电磁脉冲电缆耦合问题进行了时域求解方法的研究。引入了适用于电磁脉冲电缆耦合问题数值求解的基于细线散射的时域有限差分(FDTD)法，将Gedney's PML进行了扩展，使其可以用于各向同性有耗计算域截断问题的处理。利用建立的数值方法，模拟了电磁脉冲作用下地面铺设屏蔽电缆引起的蒙皮感应电流分布规律及波形特征，并利用辐射波电磁脉冲模拟器对该问题进行了实验研究。计算与实验结果在误差范围内的一致性证明了数值结果的可靠性，以及该时域计算方法在处理电磁脉冲电缆耦合问题的可靠性。     

有耗介质完全匹配层在时域多分辨分析中的应用

 对无耗和有耗介质中的完全匹配问题进行了研究，将广义完全匹配吸收层(GPML)应用到时域多分辨分析（MRTD）中。GPML是在扩展坐标系下由Maxwell方程得到的，在MRTD中实现对GPML的求解，并在频域对GPML进行了有效性分析，得出了GPML在不同空间步长和不同吸收层厚度情况下入射波由真空入射到吸收层的反射系数在频域的分布，并给出了有耗介质中GPML吸收效果的例子。结果表明，GPML的反射系数在一定频率范围内小于-40 dB，且随着计算空间步长的减小和吸收层厚度的增加而减小。GPML既可以用来截断无耗介质也可以用来截断有耗介质，为时域多分辨分析方法提供了一种较为通用的吸收边界。     

含负折射率介质的多层结构中倏逝波传播及隧道效应的分析

研究了倏逝波在含负折射率介质的多层平板结构中的传播特性，解析地分析了倏逝波在不同结构参数下的放大或衰减规律及其原因以及能流的分布，并着重讨论了负折射率介质的损耗对隧道效应的影响，最后通过模拟高斯光束在该结构中的传播和能量储存，形象地给出了负折射率介质的损耗对倏逝波的影响和对光子隧道效应的减弱. 关键词： 负折射率介质 倏逝波 隧道效应     

截断各向异性等离子体的修正各向异性完全匹配层吸收边界

 基于磁化等离子体本构方程,提出了一种截断各向异性色散介质的修正的各向异性完全匹配层(M-UPML)吸收边界算法。通过等效相对介电常数,将UPML推广到截断各向异性等离子体介质的情形,并推导了其时域有限差分方法(FDTD)迭代式。用该方法计算了半空间磁化与非磁化等离子体的反射系数,计算结果与解析解相一致,表明该吸收边界具有良好的吸收效果。     

截断各向异性等离子体的修正各向异性完全匹配层吸收边界北大核心CSCD

基于磁化等离子体本构方程,提出了一种截断各向异性色散介质的修正的各向异性完全匹配层(M-UPML)吸收边界算法。通过等效相对介电常数,将UPML推广到截断各向异性等离子体介质的情形,并推导了其时域有限差分方法(FDTD)迭代式。用该方法计算了半空间磁化与非磁化等离子体的反射系数,计算结果与解析解相一致,表明该吸收边界具有良好的吸收效果。     

一种增强LED光提取效率的新方法

本文从分析全内反射中的近场倏逝波出发,提出了在近场倏逝波衰减长度内置一金属Ag光栅的LED结构模型,同时基于时域有限差分(FDTD)方法计算了此模型的光谱特性,分析了此LED模型的光提取效率。结果表明置入的金属Ag光栅在特定的波段可以将近场倏逝波耦合为传播波模式辐射出去,从而有效地增强了LED的光提取效率。     

源嵌入正折射率传输线介质板内的倏逝波和成像特性

 提出了点源嵌入正折射率介质板进行亚波长成像的新方法,分析了位于负折射率媒质里的正折射率介质板内外的电压倏逝波和电压传播波分布。正和负折射率媒质分别由2维未加载传输线和2维加载电感、电容传输线网络组成。微波电路和数值仿真结果都显示由于板内增大的倏逝场,在正折射率介质板的两个界面附近出现了很大的电压幅度,该结果证实了该正折射率介质板透镜能够恢复电压倏逝波,从而提高像的分辨率。     

卷积完全匹配层在两维声波有限元计算中的应用

将基于复坐标变换和复频移扩展坐标变量的卷积完全匹配层Convolution Perfectly Machted Layer(CPML)引入到两维声波方程的有限元(FEM)计算中,该匹配层作为一种吸收边界条件Absorbing Boundary Condition(ABC)应用在有限元计算的边界截断上。文中分别给出了频域和时域的CPML方程的表达形式,并在有限元计算软件COMSOL中完成数值计算。相对于经典的PML,CPML最大的优势在于它不需要把场分裂开,这使其具有更好的稳定性和更高的吸收性能,且更易于实现。数值计算结果表明,CPML边界层有着比PML更好的吸收效果,其更有效的吸收了进入其中的声场能量。      

截断磁等离子体三维M-NPML吸收边界条件

研究三维截断磁化等离子体介质新型完全匹配层(NPML)吸收边界条件(ABC),提出应用于截断色散介质修正的M-NPML,该方法根据NPML坐标变换原理,对麦克斯韦方程中对空间偏导的变量进行坐标拉伸,得到在NPML吸收边界中修正的麦克斯韦方程组.该吸收边界只把对空间偏导的变量进行坐标拉伸,操作简单,避免了PML方法在截断普通介质时采用复杂的场分裂形式,同时比单轴各向异性完全匹配层(UPML)吸收边界截断磁化等离子体介质更加简单,编程复杂度大大降低.算例仿真结果与解析解相符,证实了该算法的有效性.     

基于非分裂FDTD的左手介质电磁特性的研究

为验证左手介质的电磁特性,采用非分裂时域有限差分方法对左手介质的Drude模型进行建模.这种方法不需要对电场和磁场进行分裂,也不需要对PML空间进行特殊处理,吸收边界PML和工作空间可以通过参数转换来完成,并且构造的PML层为有耗介质,进入PML层的透射波将迅速衰减.它是一种准确而有效的分析色散和各向异性介质的方法,通过此方法有效地验证了左手介质的负折射效应、汇聚效应、相位补偿效应,充分验证了左手介质及其反常特性的存在性和此方法分析左手介质的有效性. 关键词： 左手介质 非分裂 时域有限差分 Drude     

Discontinuous Galerkin methods for dispersive and lossy Maxwell's equations and PML boundary conditions

In this paper, we will present a unified formulation of discontinuous Galerkin method (DGM) for Maxwell's equations in linear dispersive and lossy materials of Debye type and in the artificial perfectly matched layer (PML) regions. An auxiliary differential equation (ADE) method is used to handle the frequency-dependent constitutive relations with the help of auxiliary polarization currents in the computational and PML regions. The numerical flux for the dispersive lossy Maxwell's equations with the auxiliary polarization current variables is derived. Various numerical results are provided to validate the proposed formulation.     

基于Z变换的高阶完全匹配层实现

基于拉伸坐标完全匹配层(SC-PML)公式和Z变换方法,提出以非分裂场形式来实现具有多极点的高阶完全匹配层的高效算法,来截断时域有限差分(FDTD)网格.在吸收性能方面,高阶PML同时具有传统PML和复频率偏移完全匹配层(CFS-PML)二者的优点.提供的数值算例是二维TE极化电磁波与无限长且有限宽度的理想电导体(PEC)薄片的相互作用.仿真结果显示,高阶PML公式在衰减低频行波和隐失波及减少后期反射方面效果好,比传统SC-PML和复频率偏移的卷积完全匹配层(CPML)算法有更好的吸收性能.     

Frequency domain finite-element and spectral-element acoustic wave modeling using absorbing boundaries and perfectly matched layer

Wave propagation modeling as a vital tool in seismology can be done via several different numerical methods among them are finite-difference, finite-element, and spectral-element methods (FDM, FEM and SEM). Some advanced applications in seismic exploration benefit the frequency domain modeling. Regarding flexibility in complex geological models and dealing with the free surface boundary condition, we studied the frequency domain acoustic wave equation using FEM and SEM. The results demonstrated that the frequency domain FEM and SEM have a good accuracy and numerical efficiency with the second order interpolation polynomials. Furthermore, we developed the second order Clayton and Engquist absorbing boundary condition (CE-ABC2) and compared it with the perfectly matched layer (PML) for the frequency domain FEM and SEM. In spite of PML method, CE-ABC2 does not add any additional computational cost to the modeling except assembling boundary matrices. As a result, considering CE-ABC2 is more efficient than PML for the frequency domain acoustic wave propagation modeling especially when computational cost is high and high-level absorbing performance is unnecessary.     

Near-field performance analysis of locally-conformal perfectly matched absorbers via Monte Carlo simulations

In the numerical solution of some boundary value problems by the finite element method (FEM), the unbounded domain must be truncated by an artificial absorbing boundary or layer to have a bounded computational domain. The perfectly matched layer (PML) approach is based on the truncation of the computational domain by a reflectionless artificial layer which absorbs outgoing waves regardless of their frequency and angle of incidence. In this paper, we present the near-field numerical performance analysis of our new PML approach, which we call as locally-conformal PML, using Monte Carlo simulations. The locally-conformal PML method is an easily implementable conformal PML implementation, to the problem of mesh truncation in the FEM. The most distinguished feature of the method is its simplicity and flexibility to design conformal PMLs over challenging geometries, especially those with curvature discontinuities, in a straightforward way without using artificial absorbers. The method is based on a special complex coordinate transformation which is ‘locally-defined’ for each point inside the PML region. The method can be implemented in an existing FEM software by just replacing the nodal coordinates inside the PML region by their complex counterparts obtained via complex coordinate transformation. We first introduce the analytical derivation of the locally-conformal PML method for the FEM solution of the two-dimensional scalar Helmholtz equation arising in the mathematical modeling of various steady-state (or, time-harmonic) wave phenomena. Then, we carry out its numerical performance analysis by means of some Monte Carlo simulations which consider both the problem of constructing the two-dimensional Green’s function, and some specific cases of electromagnetic scattering.     

基于辅助差分方程的完全匹配层在时域多分辨率分析算法中的应用与性能分析

将基于辅助微分方程的完全匹配层(ADE-PML)吸收边界条件引入到基于Daubechies尺度函数的时域多分辨率分析算法中. 与目前广泛应用的Berenger完全匹配层(PML)和各向异性介质完全匹配层(APML) 相比, 该吸收边界条件的实现更加容易且更节省内存. 数值结果表明, ADE-PML在吸收传播模和低频凋落模方面均优于PML和APML.     

Near-field performance analysis of locally-conformal perfectly matched absorbers via Monte Carlo simulations

In the numerical solution of some boundary value problems by the finite element method (FEM), the unbounded domain must be truncated by an artificial absorbing boundary or layer to have a bounded computational domain. The perfectly matched layer (PML) approach is based on the truncation of the computational domain by a reflectionless artificial layer which absorbs outgoing waves regardless of their frequency and angle of incidence. In this paper, we present the near-field numerical performance analysis of our new PML approach, which we call as locally-conformal PML, using Monte Carlo simulations. The locally-conformal PML method is an easily implementable conformal PML implementation, to the problem of mesh truncation in the FEM. The most distinguished feature of the method is its simplicity and flexibility to design conformal PMLs over challenging geometries, especially those with curvature discontinuities, in a straightforward way without using artificial absorbers. The method is based on a special complex coordinate transformation which is ‘locally-defined’ for each point inside the PML region. The method can be implemented in an existing FEM software by just replacing the nodal coordinates inside the PML region by their complex counterparts obtained via complex coordinate transformation. We first introduce the analytical derivation of the locally-conformal PML method for the FEM solution of the two-dimensional scalar Helmholtz equation arising in the mathematical modeling of various steady-state (or, time-harmonic) wave phenomena. Then, we carry out its numerical performance analysis by means of some Monte Carlo simulations which consider both the problem of constructing the two-dimensional Green’s function, and some specific cases of electromagnetic scattering.     

A staggered-grid finite-difference method with perfectly matched layers for poroelastic wave equations.

A particle velocity-strain, finite-difference (FD) method with a perfectly matched layer (PML) absorbing boundary condition is developed for the simulation of elastic wave propagation in multidimensional heterogeneous poroelastic media. Instead of the widely used second-order differential equations, a first-order hyperbolic leap-frog system is obtained from Biot's equations. To achieve a high accuracy, the first-order hyperbolic system is discretized on a staggered grid both in time and space. The perfectly matched layer is used at the computational edge to absorb the outgoing waves. The performance of the PML is investigated by calculating the reflection from the boundary. The numerical method is validated by analytical solutions. This FD algorithm is used to study the interaction of elastic waves with a buried land mine. Three cases are simulated for a mine-like object buried in "sand," in purely dry "sand" and in "mud." The results show that the wave responses are significantly different in these cases. The target can be detected by using acoustic measurements after processing.     

二阶声场波动方程的非分裂完全匹配层算法

在声场仿真中,完全匹配层(Perfectly Matched Layer,PML)是一种十分有效的吸收边界并得到广泛应用。为了解决基于二阶声场波动方程数值仿真中的吸收边界问题,提出了一种非分裂PML算法。首先,基于伸缩坐标变换,推导了PML算法的频域表达式。然后,通过构造辅助微分方程,得到了非分裂PML的时域表达式。最后,进行了相关理论分析和数值仿真,结果表明:相对于已有的声场分裂PML算法,该算法在保持相同的吸收效率的同时,能较大地节约存储空间,提高计算效率,且更易于实现。      

Application of convolution perfectly matched layer in finite element method calculation for 2D acoustic wave

A method was presented to extend the Convolution Perfectly Matched Layer(CPML), which bases on the complex coordinates transformation and complex frequency shifted stretched-coordinate metrics,to the 2D acoustic equation calculated with the method of Finite Element Method(FEM).This non-physical layer is used at the computational edge of a FEM as an Absorbing Boundary Condition(ABC) to truncate unbounded media.In this paper,the CPML equations have been presented in frequency domain and in time domain,respectively,and the calculations have been realized in the FEM software of COMSOL.The main advantage of CPML over the classical PML layer is that it is based on the unsplit components of the wave field leading to a more stable,highly effective absorption and a more facility to realize.The results of numerical simulation demonstrate that CPML has better absorbability than PML and it absorbs the outgoing energy more effectively.