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.     

基于等效源法和双面质点振速测量的声场分离方法

目前基于等效源法的声场分离方法有两种输入方式, 一种以双测量面上的声压为输入, 另一种以单测量面上的声压和质点振速为输入. 本文以双测量面上的质点振速为输入, 提出一种新的基于等效源法的声场分离方法. 首先给出了该方法的理论推导, 然后通过数值仿真和实验验证了该方法的有效性. 通过与基于双面声压测量的声场分离方法的比较, 证明了该方法在分离质点振速方面的优越性. 此外, 在仿真中还研究了干扰声源强度和测量面间距对分离精度的影响. 关键词： 声场分离 质点振速测量 等效源法 近场声全息     

非线性欧拉方程组的完美匹配层吸收边界条件

对于非线性Euler方程,提出一类基于完美匹配层(PML)技术的吸收边界条件。首先对线性化的Euler方程设计出PML公式,然后将线性化Euler方程中的通量函数替换成相对应的非线性通量函数,得到非线性的PML方程。考虑到PML方程中包含有一个刚性的源项,文中采用一种隐显Runge-Kutta方法来求解空间半离散后得到的ODE系统。数值实验表明设计的非线性PML吸收边界条件优于传统的特征边界条件。     

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。      

耦合微扰简正波方法与孤立子内波

水平变化环境下声场简正波解的计算精度和效率取决于本地简正波的计算方法。提出一种完备的一阶微扰理论方法,并引入迭代算法,获得了本地简正波水平波数和本征函数的精确表达式。数值结果表明,改进后的微扰简正波方法得到的简正波水平波数和本征函数精度比前人方法更高,与KRAKENC计算结果吻合较好,而计算速度比KRAKENC快100倍。同时将微扰简正波方法与耦合简正波理论结合,应用到海水声速水平变化剧烈的孤立子内波群环境。数值结果表明,该方法计算得到的传播损失与COUPLE07在单次散射近似下的计算结果吻合较好,计算速度比COUPLE07快25倍,并将该方法在声场计算中的适用频率提高到了3 kHz。      

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.     

矩形单元声场波函数构造及其应用

在波叠加法中,结构外部声场是在离散边界上对Green函数进行积分并叠加得到,但数值积分的计算效率较低。而等效源法虽然提高了计算效率,但其面源简化为点源的过程中存在较大的积分近似误差。针对上述两种方法的缺陷,构造了一种波函数以替代离散单元关于Green函数积分的声场。首先,利用球坐标系下Helmholtz方程的解,推导了替代矩形单元积分的一般形式波函数及效率更高的内推波函数。其次,当离散单元为正方形时,将其近似成圆形域,进一步简化了内推波函数的表达式。最后,将所构造的波函数应用于声场计算。数值结果表明,在计算单个矩形单元外部辐射声场时,构造的波函数不仅保证了计算精度,而且相比于直接积分大幅度提高了计算效率。其中,矩形域一般形式和内推形式的波函数计算效率是直接积分的5～6倍,圆形域内推波函数计算效率达到了直接积分的12～13倍。在简支板声源和立方箱体辐射声源数值算例中,圆形域内推波函数在整个计算频段的声场计算精度均高于等效源法。     

一种更具普适性的浅海不确定声场快速算法

非嵌入式随机多项式展开法是目前性能最优的一种不确定声场快速算法,但配点的选择对算法计算精度影响较大,且当计算随不确定海洋环境参数变化剧烈的声场输出时,需采用分段概率配点法等特殊方法处理。基于Kriging模型提出了一种新的浅海不确定声场快速算法,首先给出了该算法的理论推导,然后通过数值计算验证了算法性能,并给出具体的物理解释,结果表明:在同等条件下,新算法的计算精度较非嵌入式随机多项式展开法更高;无需针对声场输出随不确定海洋环境参数的变化情况采取特殊处理过程;克服了非嵌入式随机多项式展开法为提高计算精度将随机多项式展开至非常高的阶数,从而增加计算量的不足;较非嵌入式随机多项式展开法,其样本点的选择简单易行,且可直接计算误差,因此,本文算法较非嵌入式随机多项式展开法普适性更强。     

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。      

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。     

A novel unsplit perfectly matched layer for the second-order acoustic wave equation

When solving acoustic field equations by using numerical approximation technique, absorbing boundary conditions (ABCs) are widely used to truncate the simulation to a finite space. The perfectly matched layer (PML) technique has exhibited excellent absorbing efficiency as an ABC for the acoustic wave equation formulated as a first-order system. However, as the PML was originally designed for the first-order equation system, it cannot be applied to the second-order equation system directly. In this article, we aim to extend the unsplit PML to the second-order equation system. We developed an efficient unsplit implementation of PML for the second-order acoustic wave equation based on an auxiliary-differential-equation (ADE) scheme. The proposed method can benefit to the use of PML in simulations based on second-order equations. Compared with the existing PMLs, it has simpler implementation and requires less extra storage. Numerical results from finite-difference time-domain models are provided to illustrate the validity of the approach.     

Absorbing boundary conditions for nonlinear Euler and Navier–Stokes equations based on the perfectly matched layer technique

Absorbing boundary conditions for the nonlinear Euler and Navier–Stokes equations in three space dimensions are presented based on the perfectly matched layer (PML) technique. The derivation of equations follows a three-step method recently developed for the PML of linearized Euler equations. To increase the efficiency of the PML, a pseudo mean flow is introduced in the formulation of absorption equations. The proposed PML equations will absorb exponentially the difference between the nonlinear fluctuation and the prescribed pseudo mean flow. With the nonlinearity in flux vectors, the proposed nonlinear absorbing equations are not formally perfectly matched to the governing equations as their linear counter-parts are. However, numerical examples show satisfactory results. Furthermore, the nonlinear PML reduces automatically to the linear PML upon linearization about the pseudo mean flow. The validity and efficiency of proposed equations as absorbing boundary conditions for nonlinear Euler and Navier–Stokes equations are demonstrated by numerical examples.     

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.     

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.     

双相各向同性介质BISQ模型弹性波方程数值模拟方法

本文从Taylor级数展开式出发,推导出了交错网格一阶空间导数的任意偶数阶精度展开式和相应差分系数计算式;从本构方程和运动方程推导出了BISQ模型双相介质一阶双曲型应力-速度弹性波方程交错网格任意偶数阶精度差分格式以及推导出二维双相各向同性介质完全吸收层边界条件公式和相应的高阶交错网格差分格式。通过数值模拟研究表明,该方法边界吸收效果好,稳定性好,能够高精度模拟双相介质中地震弹性波场,且计算效率也高。     

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.     

FDTD方法分析高功率微波粗糙地面散射特性

采用时域有限差分方法(FDTD)对高功率微波(HPM)近地面传输进行了仿真,其中提出的一种完全匹配层-广义完全匹配层混合吸收边界,较好地抑制了常规FDTD方法在计算低掠射角入射时产生的边缘绕射现象。将理想水平地面数值计算结果与解析法结果对比验证计算模型的正确性,通过数值计算结果分析高功率微波粗糙地面的散射特性。理论分析和仿真结果表明:粗糙地面对散射系数变化影响较明显,从宏观角度上看,散射系数曲线同理想水平地面散射系数曲线相似,即随掠射角的增大散射系数先减小后增大;从微观角度上看,由于粗糙地面的作用,其散射系数曲线并不存在布鲁斯特角,且在某一区域并非单调增加或减小。     

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.     

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。