常规分裂和非分裂完全匹配层吸收边界比较研究

分别对常规分裂和非分裂完全匹配层吸收边界在完全弹性介质和孔隙介质的应用效果进行了比较研究。比较了两种吸收边界应用于完全弹性介质和孔隙介质所需计算量、存储量大小以及吸收效果。为比较吸收效果,首先给出两种吸收边界下声场快照图的比较,然后利用吸收边界附近的接收点波形,计算和分析了两种吸收边界在固定入射角度处随时间变化的边界反射幅度,以及对不同入射角度声波的边界反射系数。研究结果表明,无论是完全弹性介质还是孔隙介质,常规非分裂完全匹配层吸收边界比分裂完全匹配层吸收边界对垂直入射乃至一般入射角度的声波都有更好的吸收效果,但需要更大的存储量和计算量。     

孔隙介质与液体界面上波动方程数值模拟的改进 方案——MPML边界条件的应用*

由于波场数值模拟的计算区域是有限的,为了压制截断边界造成的人工边界反射,通常采用完全匹配层作为吸收边界条件。但是在含液-固界面的弹性介质中进行正演模拟时,完全匹配层边界条件容易造成稳定性方面的问题。因此,该文将多轴完全匹配层应用于该类介质的正演模拟,以改善完全匹配层边界条件引起的不稳定问题。通过在具有弹性海底的海洋环境模型以及充填液体的井孔模型中进行弹性波方程的正演模拟,分别采用传统的完全匹配层和多轴完全匹配层作为吸收边界条件,对比验证了多轴完全匹配层在含液-固界面弹性介质中数值模拟的有效性和稳定性。     

卷积完全匹配层在空爆电磁脉冲2维模拟中的应用

 在分析不同类型完全匹配层特点的基础上,选用了卷积形式完全匹配层（CPML）截断空中核爆电磁脉冲数值模拟的开放边界。从自由空间中电磁波的平面波解和分裂形式的完全匹配层出发,构造了未分裂形式的完全匹配层,应用傅里叶变换的卷积定理,推导出2维旋转椭球-双曲正交坐标系下卷积形式完全匹配层介质中电磁场的迭代形式的离散方程。计算表明,采用CPML吸收边界方法使得截断的外边界处的场的计算误差大大减少。     

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。      

基于时域有限差分算法改进卷积完全匹配层的稳定性

为了克服时域有限差分算法中卷积完全匹配层对消逝波吸收效果差的缺点,提出一种在卷积完全匹配层后添加特殊吸收层的方法.在不增加物体与吸收层内层距离的情况下,通过调节特殊吸收层中两个衰减因子,使其为常数,并令吸收因子逐层从1增加到10,来增强吸收层对消逝波的吸收性能.平面波垂直入射到单层光子晶体的算例表明,添加了特殊吸收层的吸收边界在与散射体相距5个网格的情况下仍能够保持计算结果收敛,而传统的吸收边界则需要相距80个网格才能保证结果收敛,说明该方法提高了对消逝波的吸收性能.进一步在结构中采用此吸收边界来计算多层光子晶体的传输特性曲线,并将其与常规方法计算所得结果做比较,两种结果吻合较好.数值算例验证了该方法的有效性和正确性.     

共形完全匹配层按层积分算法

基于共形完全匹配层(CPML)吸收边界,构造一种共形完全匹配层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,用多层单元剖分,以一层单元计算矩阵元素,即保留了多层单元的几何和材料信息,又减少了单元数量和计算量.数值算例表明,这种按层积分CPML吸收效果好,计算量小,可靠,高效.     

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.     

基于时域有限差分法的液晶光学特性模拟

研究了模拟光在液晶中传播的时域有限差分(FDTD)法。该方法采用完全匹配层吸收边界条件来截断计算区域,通过独立计算总场区域与散射场区域的左连接边界和右连接边界上的入射场场值来实现非周期结构的平面波波源引入,并提出了分裂场一维辅助FDTD方法来计算含有非均匀各向异性介质的边界上的入射场场值。实现了平面波源入射下具有非周期结构的液晶器件光学特性计算。对开态下扭曲向列相液晶盒的仿真结果表明,30°入射时散射区透射率的最大泄漏误差小于3%,可知该方法对非周期、非均匀各向异性介质光学特性分析是有效的。     

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。     

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.     

Frequency-dependent reflection of elastic wave from thin bed in porous media

The reflection of elastic wave from thin bed in porous media is important for oil and gas reservoir seismic exploration.The equations for calculating frequency-dependent reflection amplitude versus incident angle(FDAVA) from thin bed in porous media are obtained based on porous media theory. Some conclusions are obtained from numerical analysis, specifically, slow compression wave may be ignored when considering boundary conditions in most situations; the dispersion of reflection from thin bed is much higher than that from thick layer and is periodic in frequency domain, which is affected by the thickness of thin bed, velocity, and incident angle; the reflection amplitude envelope in frequency domain decays exponentially, which is affected by the thickness of thin bed, attenuation, and incident angle; the reflection amplitude increases with thickness of thin bed increasing, and then it decreases when the thickness reaches to a quarter of wavelength.     

An FDTD absorbing boundary condition for anisotropic media based on NPML

Based on the nearly perfectly matched layer (NPML) theory, a finite-difference time-domain (FDTD) absorbing boundary condition (ABC) is presented for truncating three-dimensional (3-D) anisotropic medium. In the proposed technique, the complex coordinate stretching in the NPML scheme and the spatial interpolation method are employed. The associated ABC formulations have the advantage of simplicity in the FDTD implementations. The radiation fields of an electric dipole in anisotropic media are calculated using the presented ABC. The results are numerically verified by the comparison with the reference solutions. Furthermore, in order to clearly show the effective absorbing performance of the proposed method, the reflection coefficient and time-dependent relative error for different layers NPML absorbing boundary are also simulated.     

Anomalous postcritical refraction behavior for certain transversely isotropic media

Snell's law at the boundary between two transversely isotropic media with a vertical axis of symmetry (VTI media) can be solved by setting up a fourth order polynomial for the sine of the reflection/transmission angles. This approach reveals the possible presence of an anomalous postcritical angle for certain transversely isotropic media. There are thus possibly three incident angle regimes for the reflection/refraction of longitudinal or transverse waves incident upon a VTI medium: precritical, postcritical/preanomalous, and postanomalous. The anomalous angle occurs for certain strongly anisotropic media where the required root to the phase velocity equation must be switched in order to obey Snell's law. The reflection/transmission coefficients, polarization directions, and the phase velocity are all affected by both the anisotropy and the incident angle. The incident critical angles are also effected by the anisotropy.     

振荡介质中平面波的反射

在复金慈堡-朗道方程描述的振荡介质中研究了平面波的反射.从理论上给出了产生反射的条件,导出了反射波和入射波这两个区域的分界线与两种介质分界线的夹角.发现两类反射,一类为回折射产生的反射,对于这类反射,理论上给出了反射角;另一类为纯反射,它与折射无关.理论分析与数值模拟结果均表明：只有当入射角大于临界入射角才会发生反射,而且反射角等于临界入射角;对于纯反射,反射角随波频率增大而增大. 关键词： 复金慈堡-朗道方程 平面波 反射     

有耗介质空间完全匹配层吸收边界条件及其应用

 针对Gedney提出的完全匹配层(PML)无法用于有耗各向同性计算域的截断及其对倏逝波的衰减不理想等问题,提出了一种扩展方法。扩展的PML的主要思想是在各向异性的PML中引入与有耗介质空间相一致的复介电常数和复磁导率,使之可以与有耗介质计算域相匹配。通过给PML的张量介电常数、张量磁导率增加衰减因子以加速倏逝波的衰减。构造了PML吸收效果验证模型,数值结果证明了扩展的PML在处理有耗介质计算域截断问题中的有效性。利用该吸收边界条件,采用时域有限差分法计算了电磁脉冲作用下地面铺设电缆的电磁脉冲响应,计算结果和试验结果取得了较好的一致。     

Deformation Features on the Free Surface and Rigid Interface during Elastic Wave Reflection

Analytical expressions defining the reflection coefficients have been derived in the framework of the known problem of elastic wave reflection from the free surface and rigid interface. The found reflection coefficients are used to analyze the dependences of different strain and rotation components during elastic wave reflection from the free surface and rigid interface in the case of ideal contact and possible slip on the wave incidence angle and elastic parameters of the medium. Deformation features of elastic media at the studied interfaces are considered for incident longitudinal and transverse waves.     

层状介质时域有限差分方法斜入射平面波引入新方式

应用二维时域有限差分方法分析层状介质中的目标散射时,在总场-散射场边界斜入射平面波源用常规方法难以引入,因为在总场-散射场边界处设置的入射波实际上包含了入射脉冲以及各分层界面的反射和多次反射.为解决这个问题,提出了斜入射平面波的混合引入方式,即对总场-散射场的四个边界面采取不同的处理方式.对于总场-散射场的纵向侧边界,用含有斜入射角度的修正一维时域有限差分方法,只要在自由空间位置加入入射脉冲就会自行产生由各分层界面形成的反射波,包括多次反射.同时,把纵向总场-散射场侧边界向下延伸,使得总场-散射场下边界位于完全匹配层内,这样透射波和散射波均为外向行波而被吸收.对于总场-散射场的上边界,由于完全位于自由空间中,边界上各点的入射波将是总场-散射场纵向边界角点处入射波的带有时间延迟的复制.数值模拟结果表明了本文所提出方法的正确性和有效性. 关键词： 时域有限差分 层状介质 斜入射平面波 修正一维麦克斯韦方程