用MEI方法研究脉冲线源辐射问题

脉冲线电流源的辐射问题是研究高功率微波辐射、传播和散射问题的基础。用时域有限差分方法结合时域MEI吸收边界条件来对该问题进行求解,通过与不同种类边界条件配合得出的数值解的比较可以证明,利用时域MEI方法的一阶吸收边界条件对线源辐射问题进行处理时,可以使截断边界离源更近,从而减少了计算量,并达到提高计算精度的目的。     

Time-Domain Analysis of Millimeter Wave Circulation Around a Magnetised Ferrite Sphere

An efficient numerical method has been devised for the study of wave circulated by a magnetised ferrite sphere. It is a finite-difference time-domain formulation that incorporates Mur's absorbing boundary conditions and a perfectly matched layer. The electromagnetic fields inside the ferrite body are calculated using special updating equations derived from the equation of motion of the magnetization vector and Maxwell's curl equations in consistency. The electromagnetic fields inside ferrite and the power-density distribution on the ferrite's surface normal to the bias external magnetic field are obtained in a wide frequency band with a single time domain run. It is observed that an incident plane wave would circulate around the magnetised ferrite body in an open space as if the ferrite were placed inside a waveguide / microstrip junction circulators.     

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.     

双重弹性波波场分离数值模拟及相关理论证明

提出一种等效的双重弹性波波场分离数值模拟方法,用于模拟纯纵波和纯横波分离模式的质点振动速度、位移以及散度场和旋度场,并将该方法应用于全弹性波波动方程数值模拟中.同时,详细推导双重弹性波波场分离波动方程的高阶交错网格有限差分数值计算公式及其稳定性条件、数值频散关系和完全匹配层(PML)吸收边界条件.理论分析和数值计算均表明,该方法可以实现高精度双重弹性波波场分离数值模拟,且纯纵波和纯横波得到完全分离,边界吸收效果较好.与前人工作相比,存储量和计算时间均得到有效改善,数值计算结果进一步验证了该方法的优越性.     

用MEI方法研究脉冲线源辐射问题

 脉冲线电流源的辐射问题是研究高功率微波辐射、传播和散射问题的基础。用时域有限差分方法结合时域MEI吸收边界条件来对该问题进行求解，通过与不同种类边界条件配合得出的数值解的比较可以证明，利用时域MEI方法的一阶吸收边界条件对线源辐射问题进行处理时，可以使截断边界离源更近，从而减少了计算量，并达到提高计算精度的目的。     

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.     

Absorbing boundary conditions for scalar waves in anisotropic media. Part 2: Time-dependent modeling

With the ultimate goal of devising effective absorbing boundary conditions (ABCs) for general anisotropic media, we investigate the well-posedness and accuracy aspects of local ABCs designed for the transient modeling of the scalar anisotropic wave equation. The ABC analyzed in this paper is the perfectly matched discrete layers (PMDL), a simple variant of perfectly matched layers (PML) that is also equivalent to rational approximation based ABCs. Specifically, we derive the necessary and sufficient condition for the well-posedness of the initial boundary value problem (IBVP) obtained by coupling an interior and a PMDL ABC. The derivation of the reflection coefficient presented in a companion paper (S. Savadatti, M.N. Guddati, J. Comput. Phys., 2010, doi:10.1016/j.jcp.2010.05.018) has shown that PMDL can correctly identify and accurately absorb outgoing waves with opposing signs of group and phase velocities provided the PMDL layer lengths satisfy a certain bound. Utilizing the well-posedness theory developed by Kreiss for general hyperbolic IBVPs, and the well-posedness conditions for ABCs derived by Trefethen and Halpern for isotropic acoustics, we show that this bound on layer lengths also ensures well-posedness. The time discretized form of PMDL is also shown to be theoretically stable and some instability related to finite precision arithmetic is discussed.     

基于压缩感知的一维海面与二维舰船复合后向电磁散射快速算法研究

矩量法作为数值方法中积分方程方法的代表, 具有计算精度高、所用格林函数自动满足辐射条件、无须额外设置边界条件等优点. 但是在舰船目标与海面复合后向电磁散射仿真中, 传统矩量法需针对每个入射角反复求解矩阵方程组, 导致其在处理后向散射问题时计算量大, 耗时长, 仿真效率低下. 为解决上述问题, 本文提出了一种基于压缩感知技术的矩量法的改进算法. 该算法在求解复合后向散射问题时, 首先利用观测矩阵与传统矩量法中的电压矩阵相乘, 得到一组新的低维度的电压矩阵; 其次通过求解新电压矩阵下的矩阵方程组, 获得电流矩阵的观测值; 最后利用恢复算法(本文采用正交匹配追踪算法)重构出所需的原始入射源照射下的电流系数. 通过与传统矩量法的计算结果对比, 表明本文所提算法能够在保证计算精度的前提下, 明显减少计算时间, 提高计算效率.     

旋转体时域有限差分法的另一推导方法和单向波方程吸收边界条件

提出了旋转体时域有限差分法的另一推导方法.基于这一方法,推导了旋转体电磁波的波动方程,进一步得出了旋转体时域有限差分法的单向波方程吸收边界条件.数值实验证实了该吸收边界条件的正确性.     

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。     

一种适用于任意阶空间差分时域有限差分方法的色散介质通用吸收边界条件算法

基于伸展坐标完全匹配层方程和辅助微分方程 方法, 给出了一种在时域有限差分(FDTD) 计算中适用于常见色散介质的通用边界条件算法. 该算法适用于任意阶的FDTD空间差分, 并且由于所采用的D-H方程独立于计算区域, 所以可以被用于截断任意电介质. 数值试验结果表明, 与卷积完全匹配层 算法相比较, 所提出的吸收边界条件算法不仅通用性强、 计算复杂度低、 计算时间短, 并且吸收效果有明显的提高.     

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。     

FDTD Analysis of EW Wave Circulating by a Magnetized Ferrite Body in Free Space

An efficient numerical method has been devised for the study of wave circulating by a magnetised ferrite body of an arbitrary shape. It is a finite-difference time-domain formulation that incorporates Mur's absorbing boundary conditions and a perfectly matched layer. Several shapes of interest have been studied, including spheres, circular cylinders. The electromagnetic fields inside ferrite and the power-density distribution on the ferrite's surface normal to the bias external magnetic field are obtained. It is observed that an incident plane wave would circulate around the magnetised ferrite body in an open space as if the ferrite were placed inside a waveguide junction circulator.     

Studies on Fast Algorithm for the Scattering of a Large Array of Waveguide-Fed Wide-Slot Antennas in Millimeter Wave Region

We present an effective numerical technique to characterize the scattering of wide-slot antennas fed by waveguides with arbitrary terminations in terms of the method of moment (MoM) and the mixed potential integral equation (MPIE). In particular, the precorrected-fast Fourier transform (P-FFT) eliminates the need to generate and store the usual square impedance matrix andthus leads to speed up the matrix-vector multiplication in the resultant system. This property makes the Rao-Wilton-Glisson (RWG) functions to be useful in simulating electrically large-scale problems. In addition, the scattering from the finite ground surfaces is accounted for in the total scattered field by using the method of equivalent edge currents. The numerical results are presented and compared with both the traditional method of moment results obtained using the entire-domain basis functions and the experimental results, to demonstrate the proposed method to be a good candidate for study on the scattering of arbitrary wide-slot large array.     

Simulation of electromagnetic scattering by random discrete particles using a hybrid FE-BI-CBFM technique

A hybrid finite element–boundary integral–characteristic basis function method (FE-BI-CBFM) is proposed for an efficient simulation of electromagnetic scattering by random discrete particles. Specifically, the finite element method (FEM) is used to obtain the solution of the vector wave equation inside each particle and the boundary integral equation (BIE) using Green's functions is applied on the surfaces of all the particles as a global boundary condition. The coupling system of equations is solved by employing the characteristic basis function method (CBFM) based on the use of macro-basis functions constructed according to the Foldy–Lax multiple scattering equations. Due to the flexibility of FEM, the proposed hybrid technique can easily deal with the problems of multiple scattering by randomly distributed inhomogeneous particles that are often beyond the scope of traditional numerical methods. Some numerical examples are presented to demonstrate the validity and capability of the proposed method.     

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。     

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。     

X波段六腔渡越管振荡器的高频特性研究

从麦克斯韦方程出发,采用时域有限差分法（FDTD）和离散傅里叶变换（DFFT）相结合的方法,通过数值计算得出了六腔开放式谐振腔中前四个谐振频率和场分布,计算出的谐振频率与实验测量结果基本相同。比较了开放腔和封闭腔谐振频率,验证了TEM波吸收边界条件,并在实际编程计算中得以应用。计算结果为六腔渡越管振荡器的机理研究提供了依据。     

Boundary element-free method for elastodynamics

1 Introduction In recent years, more and more attention has been paid to researches on the meshless (or meshfree) method, which makes it a hot direction of computational mechanics[1,2]. The meshless method is the approximation based on nodes, then the large deformation and crack growth problems can be simulated with the method without the re-meshing technique. And the meshless method has some advantages over the traditional computa- tional methods, such as finite element method (FEM) and boun…     

Boundary element-free method for elastodynamics

The moving least-square approximation is discussed first. Sometimes the method can form an ill-conditioned equation system, and thus the solution cannot be obtained correctly. A Hilbert space is presented on which an orthogonal function system mixed a weight function is defined. Next the improved moving least-square approximation is discussed in detail. The improved method has higher computational efficiency and precision than the old method, and cannot form an ill-conditioned equation system. A boundary element-free method (BEFM) for elastodynamics problems is presented by combining the boundary integral equation method for elastodynamics and the improved moving least-square approximation. The boundary element-free method is a meshless method of boundary integral equation and is a direct numerical method compared with others, in which the basic unknowns are the real solutions of the nodal variables and the boundary conditions can be applied easily. The boundary element-free method has a higher computational efficiency and precision. In addition, the numerical procedure of the boundary element-free method for elastodynamics problems is presented in this paper. Finally, some numerical examples are given.