用时域有限差分法计算透声目标的散射场

在透声界面附近运用声学基本方程可导出边界条件的时域有限差分（ＦＤＴＤ）表达式。本文用ＦＤＴＤ计算透声物体的反射、透射和散射，并讨论全内反射和完全透射现象，所得到的结果与理论解相符合，从而验证了这一边界条件差分表达式的适用性。基于此边界条件的ＦＤＴＤ基本框架可望在解决各种非弹性体的散射问题中有广泛的应用。本文还给出一个有效的吸收边界条件     

Formulation and validation of Berenger's PML absorbing boundary forthe FDTD simulation of acoustic scattering

Berenger's perfectly matched layer (PML) absorbing boundary condition for electromagnetic (EM) waves is derived to absorb 2-D and 3-D acoustic waves in finite difference time domain (FDTD) simulation of acoustic wave propagation and scattering. A PML medium suitable for acoustic waves is constructed. Plane wave propagation in the PML medium is solved for both 2-D and 3-D cases and explicit FDTD boundary conditions are derived. The equations show that a matched PML medium is a perfect simulation of free space in that a plane wave does not change its direction of propagation or its speed when it propagates from free space into a matched PML medium. FDTD simulation of a pulsed point source propagating in two dimensions is carried out to test the performance of the PML boundary for acoustic waves. Results show that an eight layer PML boundary condition reduces the reflected error 40 dB over Mur's second order boundary condition     

插值小波自适应求解层状介质波传问题

利用多尺度插值小波理论,提出一种适合于求解一般边界层状介质波传问题的快速自适应配点算法。将问题放在多尺度插值空间中进行,其插值小波系数与物理空间点一一对应,可简单快速地处理非线性、边界等。使非均匀变化的响应得到自适应压缩存储,改善了计算效率。地震勘探中数值实例显示了方法良好的潜力。     

Electrodynamics of layered media with boundary conditions corresponding to the total-current continuum

A consistent physical and mathematical model of propagation of electromagnetic waves in layered media, in which the induced surface charge is not explicitly taken into account, has been constructed on the basis of Maxwell equations, the total-current continuum equation, and the Dirichlet theorem. A numerical method of through counting for solving the system of equations defining layered media has been developed and substantiated. Examples of numerical simulation of the propagation of an electromagnetic wave in a two-dimensional cellular structure and the propagation of a modulated signal in a one-dimensional layered medium on condition that the current flows at the interfaces between the adjacent media are dependent are presented.     

求解弹性波有限差分法中自由边界处理方法的对比

自由边界条件在计算方法中的数值表征是地震波模拟中的一个重要内容,表征的有效性直接关系到所得波场能否代表地表介质特性的真实响应。该文评估了交错网格有限差分法中5 种常用自由边界处理方法:直接法、应力镜像法、改进应力镜像法、横向各向同性介质替换法和声学边界替换法,并与有限元法模拟结果进行了对比,波形曲线直观比较及波幅比与相关系数定量比较显示横向各向同性介质替换法与有限法模拟结果一致性最好。进一步的层状介质模型弹性波数值模拟结果表明:横向各向同性介质替换法的精度和可靠性最高,能真实表征地表介质中的地震波传播。     

Finite difference time domain methods for piezoelectric crystals

The numerical simulation of acoustic wave propagation through piezoelectric crystals using the finite-difference time-domain (FDTD) method is introduced. The update equations for the velocity and stress fields are derived and applied to the propagation of ultrasonic waves in three substrates. The concept of the perfectly matched layer (PML), first introduced for the simulation of electromagnetic waves, is extended to the simulation of mechanical waves. The technique is shown to be effective for some crystals, but the PML is found to exhibit numerical instabilities for others.     

Propagation properties of ultrashort pulsed bessel beams in dispersive media

A detailed study of ultrashort pulsed Bessel beams in linear dispersive media is performed. The spatial and temporal parts of pulsed Jn beams are separable in dispersive media, provided that the parameter a is independent of frequency omega. The spatial part keeps the Jn shape unchanged during propagation. The temporal evolution behavior of pulsed Jn beams depends on the material's dispersion and diffraction. The pulses can be broadening and become negatively chirped while propagating in anomalous dispersive media. In normal dispersive media, the pulses can be broadening and positively or negatively chirped; even dispersion-free propagation can be achieved if the beam and material parameters are suitably chosen. The condition under which higher-order dispersive effects can be neglected is also discussed.     

Comparative study on orthotropic solid waves by time-domain BEM and dynamic photoelasticity

Experimental research and numerical analysis are two basic tools in the study of wave propagation problems in orthotropic media. In this paper, an experimental method, namely dynamic orthotropic photoelasticity, which studies the dynamic behavior of orthotropic materials on a macroscopic scale by employing orthotropic birefringent materials, is established. Meanwhile, a numerical method, namely time domain boundary element method (BEM) for wave propagation in orthotropic media, is also presented. The two methods are used together in the analysis of semi-infinite orthotropic plates with and without a circular hole modeled by a unidirectional fiber-reinforced composite under impact loading. The propagation, reflection and diffraction of stress waves in the orthotropic media are recorded experimentally and investigated. Time histories of birefringent fringe orders or stresses for specific points of the plates are obtained, respectively, from the two methods and compared with each other. The comparative study demonstrates the applicability and accuracy of the two methods for wave propagation problems in orthotropic media.     

Finite-difference time-domain solution of light scattering by dielectric particles with a perfectly matched layer absorbing boundary condition

A three-dimensional finite-difference time-domain (FDTD) program has been developed to provide a numerical solution for light scattering by nonspherical dielectric particles. The perfectly matched layer (PML) absorbing boundary condition (ABC) is used to truncate the computational domain. As a result of using the PML ABC, the present FDTD program requires much less computer memory and CPU time than those that use traditional truncation techniques. For spheres with particle-size parameters as large as 40, the extinction and absorption efficiencies from the present FDTD program match the Mie results closely, with differences of less than ~1%. The difference in the scattering phase function is typically smaller than ~5%. The FDTD program has also been checked by use of the exact solution for light scattering by a pair of spheres in contact. Finally, applications of the PML FDTD to hexagonal particles and to spheres aggregated into tetrahedral structures are presented.     

Causality in propagation of a pulse in a nonlinear dispersive medium

We investigate the causal propagation of the pulse through dispersive media by very precise numerical solution of the coupled Maxwell–Bloch equations without any approximations about the strength of the input field. We study full nonlinear behaviour of the pulse propagation through solid state media like ruby and alexandrite. We have demonstrated that the information carried by the discontinuity, i.e. front of the pulse, moves inside the media with velocity c even though the peak of the pulse can travel either with sub-luminal or with super-luminal velocity. Our numerical demonstration is subject to the condition that the background refractive index of the medium is unity. We extend the argument of Levi-Civita to prove that the discontinuity would travel with velocity c even in a nonlinear medium.     

A k-space method for moderately nonlinear wave propagation

A k-space method for moderately nonlinear wave propagation in absorptive media is presented. The Westervelt equation is first transferred into k-space via Fourier transformation, and is solved by a modified wave-vector time-domain scheme. The present approach is not limited to forward propagation or parabolic approximation. One- and two-dimensional problems are investigated to verify the method by comparing results to analytic solutions and finite-difference time-domain (FDTD) method. It is found that to obtain accurate results in homogeneous media, the grid size can be as little as two points per wavelength, and for a moderately nonlinear problem, the Courant-Friedrichs-Lewy number can be as large as 0.4. Through comparisons with the conventional FDTD method, the k-space method for nonlinear wave propagation is shown here to be computationally more efficient and accurate. The k-space method is then employed to study three-dimensional nonlinear wave propagation through the skull, which shows that a relatively accurate focusing can be achieved in the brain at a high frequency by sending a low frequency from the transducer. Finally, implementations of the k-space method using a single graphics processing unit shows that it required about one-seventh the computation time of a single-core CPU calculation.     

3D elastic wave propagation modelling in the presence of 2D fluid-filled thin inclusions

In this paper, the traction boundary element method (TBEM) and the boundary element method (BEM), formulated in the frequency domain, are combined so as to evaluate the 3D scattered wave field generated by 2D fluid-filled thin inclusions. This model overcomes the thin-body difficulty posed when the classical BEM is applied. The inclusion may exhibit arbitrary geometry and orientation, and may have null thickness. The singular and hypersingular integrals that appear during the model's implementation are computed analytically, which overcomes one of the drawbacks of this formulation. Different source types such as plane, cylindrical and spherical sources, may excite the medium. The results provided by the proposed model are verified against responses provided by analytical models derived for a cylindrical circular fluid-filled borehole.The performance of the proposed model is illustrated by solving the cases of a flat fluid-filled fracture with small thickness and a fluid-filled S-shaped inclusion, modelled with both small and null thickness, all of which are buried in an unbounded elastic medium. Time and frequency responses are presented when spherical pulses with a Ricker wavelet time evolution strikes the cracked medium. To avoid the aliasing phenomena in the time domain, complex frequencies are used. The effect of these complex frequencies is removed by rescaling the time responses obtained by first applying an inverse Fourier transformation to the frequency domain computations. The numerical results are analysed and a selection of snapshots from different computer animations is given. This makes it possible to understand the time evolution of the wave propagation around and through the fluid-filled inclusion.     

吸收边界条件下散射波场模拟及其误差分析研究

研究了一种通过Sommerfeld辐射条件建立的吸收边界条件,并由此引入吸收边界算子,结合有限元数值方法,模拟了无限区域非均匀介质中的近场散射问题,对误差的主要来源也作了一些分析。这种吸收边界条件具有解耦特性,简化了计算,且近似程度较高,数值计算结果与解析结果的比较表明了良好的吸收效果。另外有限元方法的应用,使其可灵活运用于具有一般几何形状的散射体和多个散射体情况     

A k-space method for large-scale models of wave propagation in tissue

Large-scale simulation of ultrasonic pulse propagation in inhomogeneous tissue is important for the study of ultrasound-tissue interaction as well as for development of new imaging methods. Typical scales of interest span hundreds of wavelengths. This paper presents a simplified derivation of the k-space method for a medium of variable sound speed and density; the derivation clearly shows the relationship of this k-space method to both past k-space methods and pseudospectral methods. In the present method, the spatial differential equations are solved by a simple Fourier transform method, and temporal iteration is performed using a k-t space propagator. The temporal iteration procedure is shown to be exact for homogeneous media, unconditionally stable for “slow” (c(x)⩽c₀) media, and highly accurate for general weakly scattering media. The applicability of the k-space method to large-scale soft tissue modeling is shown by simulating two-dimensional propagation of an incident plane wave through several tissue-mimicking cylinders as well as a model chest wall cross section. A three-dimensional implementation of the k-space method is also employed for the example problem of propagation through a tissue-mimicking sphere. Numerical results indicate that the k-space method is accurate for large-scale soft tissue computations with much greater efficiency than that of an analogous leapfrog pseudospectral method or a 2-4 finite difference time-domain method. However, numerical results also indicate that the k-space method is less accurate than the finite-difference method for a high contrast scatterer with bone-like properties, although qualitative results can still be obtained by the k-space method with high efficiency. Possible extensions to the method, including representation of absorption effects, absorbing boundary conditions, elastic-wave propagation, and acoustic nonlinearity, are discussed     

Parallel implementation of the biorthogonal multiresolution time-domain method

The three-dimensional biorthogonal multiresolution time-domain (Bi-MRTD) method is presented for both free-space and half-space scattering problems. The perfectly matched layer (PML) is used as an absorbing boundary condition. It has been shown that improved numerical-dispersion properties can be obtained with the use of smooth, compactly supported wavelet functions as the basis, whereas we employ the Cohen-Daubechies-Fouveau (CDF) biorthogonal wavelets. When a CDF-wavelet expansion is used, the spatial-sampling rate can be reduced considerably compared with that of the conventional finite-difference time-domain (FDTD) method, implying that larger targets can be simulated without sacrificing accuracy. We implement the Bi-MRTD on a cluster of allocated-memory machines, using the message-passing interface (MPI), such that very large targets can be modeled. Numerical results are compared with analytical ones and with those obtained by use of the traditional FDTD method.     

Modified piecewise linear current density recursive convolution finite-difference timedomain method for anisotropic magnetised plasmas

A modified piecewise linear current density recursive convolution (PLCDRC) finite-difference time-domain (FDTD) for anisotropic magnetised plasma is proposed. The method is derived using two recursive conclusion. The electric field is time-shifted in the first convolution and the current density is time-shifted in the second convolution. The computation of the current density and the electric field employ the piecewise linear approximation technique. Like PLCDRC FDTD, the method has more accuracy over CDRC FDTD. Moreover, it is faster in computation velocity than PLCDRC FDTD. The high efficiency and accuracy of the method are confirmed by computing the reflection and transmission through a magnetised plasma layer, with the direction of propagation parallel to the direction of the biasing field. The bistatic radar cross-section of conducting sphere covered with magnetised plasma is also calculated. Then, the numerical dispersion relation of the new PLCDRC FDTD scheme is derived. The numerical dispersion error and dissipation error caused by the new PLCDRC-FDTD method are investigated by comparing the real and imaginary parts of the numerical wave number with those of the analytical wave number. Finally, the stability of the new PLCDRC-FDTD method is discussed. This method can also be used in other frequency dispersion electromagnetic problem if it is modified slightly.     

Propagation of partially coherent twisted anisotropic Gaussian Schell-model beams in dispersive and absorbing media

By adopting a new tensor method, we derived an analytical propagation formula for the cross-spectral density of partially coherent twisted anisotropic Gaussian Schell-model (GSM) beams through dispersive and absorbing media. Using the derived formula, we studied the evolution properties and spectrum properties of twisted anisotropic GSM beams in dispersive and absorbing media. The results show that the dispersive and absorbing media have strong influences on the propagation properties of twisted anisotropic GSM beams and their spectrum evolution. Our method provides a simple and convenient way to study the propagation of twisted anisotropic GSM beams in media with complex refractive index.     

Finite-difference time-domain analysis of frequency-selective surfaces in the mid-infrared

We use the finite-difference time-domain (FDTD) method to model the spectral properties of frequency-selective surfaces (FSSs) at normal incidence in the 1-10 microm wavelength. At these wavelengths the usual assumption that the metallic portions of a FSS are infinitesimally thin perfect conductors are no longer valid. We include the effects of dispersive complex conductivity for real metals and dispersive permittivity for dielectric materials by developing a unified approach that is especially suited for use in FDTD simulations. We concentrate on the finite nature of the metallic conductivity and its variation with wavelength in FSS structures. Our simulation results indicate that the resonant spectrum of a FSS in this wavelength range depends not only on the geometry of the structure and the dielectric substrate present, but also critically on the dispersive properties of the metal species used for the conductors.     

“Causal” shape functions in the time domain boundary element method

Since failing to respect the causality condition has been identified as one of the main sources of inaccuracies in the time domain boundary element method for elastodynamics and scalar wave propagation problems, in this contribution new shape functions are investigated, which permit a more accurate simulation of the continuous propagation of wave fronts. The performance of these shape functions in 2D scalar wave propagation problems is tested both for the potential (displacement) and for the time gradient (velocity) equations. Analytical time integrations are developed and numerical results are presented.     

Wave propagation in fibre reinforced composite plate with circular hole under impact loading

Abstract

In this paper, experimental and numerical methods have been applied to the study of composite dynamics. Dynamic orthotropic photoelasticity is employed in the experimental work and the time domain boundary element method for anisotropic media is adopted for the numerical analysis. A fibre reinforced birefringent composite plate is used to model the semi-infinite orthotropic domain with a circular hole. A rifle bullet was used to exert the impact loading with the loading direction parallel and perpendicular to the fibre direction. In the experiments, the propagation, reflection, and diffraction of the stress wave around the hole were recorded and the results were analysed. The time histories of the stress components were obtained from the same experiments and compared with the results from the corresponding computations carried out using the time domain boundary element method. Some valuable data regarding composite dynamics and associated engineering implications were obtained. The comparative study also demonstrates the applicability and accuracy of the two methods for wave propagation problems in orthotropic media.