快速多极边界元法用于扩散光学断层成像研究

在求解扩散光学断层成像中的正向问题时, 目前普遍采用有限元法, 但是随着实际模型规模的增大, 有限元法的计算量问题日益显著, 而边界元法则由于可以降低计算维度使计算量减少而备受关注. 本文以均匀的高散射介质为模型, 研究了将快速多极边界元法用于扩散光学断层成像的正向问题. 快速多极边界元法利用核函数的多极展开, 将常规边界元法中系数矩阵和迭代矢量的乘积项等价为相应四叉树结构的一次递归, 再结合广义最小残量法进行迭代求解. 将计算结果和蒙特卡罗法的模拟结果进行了比较, 表明利用快速多极边界元法的模拟结果和蒙特卡罗法的结果有很好的一致性. 研究结果验证了快速多极边界元法可以用于扩散光学断层成像, 为其大规模和实时成像带来可观的前景. 关键词： 扩散光学断层成像 边界元法 快速多极边界元法     

有限元/边界元耦合方法在海洋生物目标强度特性研究的应用*

目标强度特性是海洋生物声学识别与资源量评估的重要依据,其中,基于近似几何体和声阻抗特性的理论模型法是研究海洋生物目标强度的重要手段。由于对几何形态近似处理以及数值求解方法的限制,传统理论模型对声波频率、入射方位以及目标声阻抗、形态尺寸等均有各自不同的适用范围,单一模型难以满足不同种类或同一种类但不同尺寸海洋生物的目标强度求解。本文尝试将逐渐见诸应用的有限元/边界元耦合方法用于海洋生物目标强度特性研究,分别以球形生物、纺锤形鱼类尾明角灯鱼(Ceratoscopelus warmingii)和细长形浮游动物南极大磷虾(Euphausia superba)为例进行仿真计算,并与相适应的经典理论模型进行对比分析。结果表明,对于球形生物,有限元/边界元耦合方法与解析模型的目标强度频响曲线完全吻合;对于纺锤形鱼类,有限元/边界元耦合方法可有效弥补基于模态级数解的形变圆柱体模型在中低频和两端入射时的准确性问题;对于细长形浮游动物,有限元/边界元耦合方法与畸变波玻恩近似模型高度吻合。综上,有限元/边界元耦合方法对多种海洋生物目标强度求解均具有较好的适用性,未来有待进一步结合实验测定进行验证。     

A coupled edge-/face-based smoothed finite element method for structural-acoustic problems

The edge-based smoothed finite element method (ES-FEM) and the face-based smoothed finite element method (FS-FEM) developed recently have shown great efficiency in solving solid mechanics problems with triangular and tetrahedral meshes. In this paper, a coupled ES-/FS-FEM model is extended to solve the structural-acoustic problems consisting of a plate structure interacting with the fluid medium. Three-node triangular elements and four-node tetrahedral elements are used to discretize the two-dimensional (2D) plate and three-dimensional (3D) fluid, respectively, as they can be generated easily and even automatically for complicated geometries. The field variable in each element is approximated using the linear shape functions, which is exactly the same as that in the standard FEM. The gradient field of the problem is obtained particularly using the gradient smoothing operation over the edge-based and face-based smoothing domains in 2D and 3D, respectively. The gradient smoothing technique can provide a proper softening effect to the model, effectively solve the problems caused by the well-known “overly-stiff” phenomenon existing in the standard FEM, and hence significantly improve the accuracy of the solution for the coupled systems. Intensive numerical studies have been conducted to verify the effectiveness of the coupled ES-/FS-FEM for structural-acoustic problems.     

Development of a finite element model for coupled radiative and conductive heat transfer in participating media

Considering the geometrical applicability, a finite element model (FEM) for coupled radiative-conductive heat transfer has been developed which is applicable to enclosures of arbitrary geometry in present research. The present work provides a solution of coupled heat transfer in a rectangular, cylindrical or annulus enclosure with black or gray walls containing an absorbing-emitting-scattering medium. It is also applied to study the influence of conductive/radiation coefficient, albedo and wall emissivity on the temperature distribution in the medium. Compared with the results available in other references, the present FEM has no limitation with respect to geometry and can predict the coupled radiative-conductive heat transfer in participating media accurately.     

A prediction of the acoustic field of a vibrating box by FEM-BEM

I.Mathematicalmodelofacousticfie1dByapplyingtheSommerfeldradiationcondihonThus,anacousticfic1disdescribcdbyHelmholtzformula.Byconsideringaficldpointinthearea,Helmholtzformulaisgivenbythefollowingthreeintegra1equations:(1)Theexternalintcgra1fOrmu1a'(2)Thcintcrnalintegralformu1af(3)Thesurfaceintegralformu1afwhcreP.isthesoundpressureonthcSsurface;rthedistancefrompointqtothee1ementsurfacedSiqtheficldpoint,tuthefrcqucncyoftheacousticradiation;pthedensityofthesurroundingmedium,vsthenormalvibrati…     

Numerical analysis of immersed finite cylindrical shells using a coupled BEM/FEM and spatial spectrum approach

This study numerically analyzes submerged cylindrical shells using a coupled boundary element method (BEM) with finite element method (FEM) in conjunction with the wave number theory, in which the spatial Fourier transform of surface velocity for cylinders is directly related to pressure in a far field. The acoustic loading is formulated using a symmetric complex matrix derived from a boundary integral equation where the symmetry is based on an acoustic reciprocal principle for surface acoustics. In this formulation the acoustic loading matrix is a large acoustic element whose degree of freedom is connected to the normal displacement of the vibrating structures. The coupled BEM/FEM equation is a banded, symmetric matrix, and thus its bandwidth can be minimized using a proper algorithm. This formulation significantly increases numerical efficiency. The computed normal velocity is thus transformed to wave number representation to examine acoustic radiation. A finite plane cylindrical shell, without attached stiffeners, and a shell with internal ring stiffeners are chosen to demonstrate the present analysis procedure. The far field pressure computed directly from the integral equation and predicted by wave number theory correlates closely with increasing vibrating frequency. Meanwhile, the influences of the internal ring structures on acoustic radiation are examined using the wave number theory, which helps in understanding how internal structures influence radiated noise.     

Parameters Extraction of Millimeter Wave Circuits by Hybrid Vector Finite Element and Moment Method Combined with SOC Technique

This paper presents a hybrid method, which couples the vector finite element method (FEM) and method of moment (MOM) for analyzing the field and current distribution of the millimeter wave circuits. The FEM is applied to handle the interior region of dielectric bodies and MOM is used to solve surface integral equations. Then, These integral expressions are coupled into the FEM equations through the continuity of the tangential fields across the connection boundaries. Simultaneously, the short-open calibration (SOC) technique is used for predicting accurately the scattering parameters of the circuits. Numerical results are well compared with those published in the previous literatures.     

Fluid-Structure Interaction in Microchannel Using Lattice Boltzmann Method and Size-Dependent Beam Element

Fluid-structure interaction (FSI) problems in microchannels play prominent roles in many engineering applications. The present study is an effort towards the simulation of flow in microchannel considering FSI. Top boundary of the microchannel is assumed to be rigid and the bottom boundary, which is modeled as a Bernoulli-Euler beam, is simulated by size-dependent beam elements for finite element method (FEM) based on a modified couple stress theory. The lattice Boltzmann method (LBM) using D2Q13 LB model is coupled to the FEM in order to solve fluid part of FSI problem. In the present study, the governing equations are non-dimensionalized and the set of dimensionless groups is exhibited to show their effects on micro-beam displacement. The numerical results show that the displacements of the micro-beam predicted by the size-dependent beam element are smaller than those by the classical beam element.     

A coupled solid–fluid method for modelling subduction

We present a novel dynamic approach for solid–fluid coupling by joining two different numerical methods: the boundary-element method (BEM) and the finite element method (FEM). The FEM results describe the thermomechanical evolution of the solid while the fluid is solved with the BEM. The bidirectional feedback between the two domains evolves along a Lagrangian interface where the FEM domain is embedded inside the BEM domain. The feedback between the two codes is based on the calculation of a specific drag tensor for each boundary on finite element. The approach is presented here to solve the complex problem of the descent of a cold subducting oceanic plate into a hot fluid-like mantle. The coupling technique is shown to maintain the proper energy dissipation caused by the important secondary induced mantle flow induced by the lateral migrating of the subducting plate. We show how the method can be successfully applied for modelling the feedback between deformation of the oceanic plate and the induced mantle flow. We find that the mantle flow drag is singular at the edge of the retreating plate causing a distinct hook shape. In nature, such hooks can be observed at the northern end of the Tonga trench and at the southern perimeter, of the South American trench.     

微波元件与加速结构的有限元分析

研究了有限元方法在二维均匀结构和轴对称加速结构中的应用,采用了带宽优化技术和子空间求解特征值方法,并给出了部分例子,结果表明该方法精度高、速度快.这些方法可直接用于三维程序、并行计算.     

超声波检测计算机模拟和仿真的研究及应用现状

随着高性能计算机的广泛应用，超声检测模拟和仿真的研究方兴未艾。本文对这些研究所选择的数学模型和方法进行了综合评述，探讨了Gaussiam模型、声线模型、衍射理论、有限积分技术等的应用，涉及的方法包括各种解析方法及有限差分、有限元、边界元等数值方法。     

Forward and inverse problem for cardiac magnetic field and electric potential using two boundary element methods

This paper discusses the forward and inverse problem for cardiac magnetic fields and electric potentials.A torso-heart model established by boundary element method(BEM) is used for studying the distributions of cardiac magnetic fields and electric potentials.Because node-to-node and triangle-to-triangle BEM can lead to discrepant field distributions,their properties and influences are compared.Then based on constructed torso-heart model and supposed current source functional model-current dipole array,the magnetic and electric imaging by optimal constrained linear inverse method are applied at the same time.Through figure and reconstructing parameter comparison,though the magnetic current dipole array imaging possesses better reconstructing effect,however node-to-node BEM and triangleto-triangle BEM make little difference to magnetic and electric imaging.     

Comparison and implementation of the various numerical methods used for calculating transmission loss in silencer systems

Issues concerning the design and use of large-scale silencers are more prevalent today then ever before. With the increased use of large industrial machinery (such as gas turbines) and the increase in public awareness and concern for noise control, the desire to be able to properly design silencers for specific applications is increasing. Even today, most silencer design is performed by simply modifying existing designs without full confidence of the new performance characteristics. Due to the size and expense of these silencers, it would be beneficial to have means to predict the insertion loss (IL) or transmission loss (TL) characteristics at the design stage. To properly accomplish this, many factors such as geometry, absorptive material properties, flow effects, break out noise, and self-generated noise must be considered. The use of the finite element method (FEM) and the boundary element method (BEM) can aid in the prediction and design. This paper examines three of the different methods used in calculation of TL values; namely the “traditional” laboratory method, the 4-pole transfer matrix method and the 3-point method. A comparison of these methods based on such criteria as accuracy, computation time, and ease of use was conducted. In addition, the idiosyncrasies and problems encountered during implementation are presented. The conclusions were that the FEM is better suited for this kind of application and that the 3-point method was the fastest method and was easier to use than the 4-pole method.     

轨道交通箱型梁腔室结构的减振降噪研究

轨道交通箱型梁在列车荷载作用下产生的低频振动与噪声对人体健康危害很大,针对箱型梁的减振降噪研究具有重要意义。将有限元振动分析理论与声辐射分析边界元法相结合,计算列车荷载作用下箱型梁的结构噪声,并对比分析不同的腔室结构对箱型梁结构噪声辐射的影响。计算结果表明:箱型梁场点结构噪声的辐射受振动水平影响较大;对于不同的腔室结构的箱型梁,跨中场点的最大线性声压级从大到小依次为单箱单室、单箱双室、单箱三室、双箱单室箱型梁;箱型梁采用双箱单室结构形式最有利于结构噪声的控制,且随辐射距离的增加,噪声辐射衰减越快;降低翼缘和腹板振动水平能够有效降低箱型梁结构噪声。分析结果可为城市轨道交通箱型梁的结构减振降噪设计提供一定的理论参考。     

Simulation of fluid-structure interaction in a microchannel using the lattice Boltzmann method and size-dependent beam element on a graphics processing unit

Fluid-structure interaction （FSI） problems in microchannels play a prominent role in many engineering applications. The present study is an effort toward the simulation of flow in microchannel considering FSI. The bottom boundary of the microchannel is simulated by size-dependent beam elements for the finite element method （FEM） based on a modified cou- ple stress theory. The lattice Boltzmann method （LBM） using the D2Q13 LB model is coupled to the FEM in order to solve the fluid part of the FSI problem. Because of the fact that the LBM generally needs only nearest neighbor information, the algorithm is an ideal candidate for parallel computing. The simulations are carried out on graphics processing units （GPUs） using computed unified device architecture （CUDA）. In the present study, the governing equations are non-dimensionalized and the set of dimensionless groups is exhibited to show their effects on micro-beam displacement. The numerical results show that the displacements of the micro-beam predicted by the size-dependent beam element are smaller than those by the classical beam element.     

边界元素法在NSRL束测系统调试中的应用

 讨论了边界元素法（BEM）及其在NSRL束流位置监测器（BPM）[1]测试中的应用。计算了BPM探头的灵敏度,以此检验模拟定标测试数据的可信程度。作为该方法的进一步探讨,尝试了由模拟程序直接计算出有机械加工误差时的灵敏度,给出了机械加工要求的参考。     

应用有限元和边界元法计算方坯软接触结晶器的电磁场

给出了用有限元和边界元相结合的方法计算方坯软接触结晶器内钢液电磁场分布的全过程,并对4面体单元基础上的Whitney边元素,H-Φ方程及边界积分方程的离散方法作了重点解释.采用有限元和边界元相结合的方法来计算电磁场的分布可以大大减少计算工作量和计算时间.自行开发了三维电磁场计算程序,将数值模拟结果与物理实际进行了比较.     

COMBINATION OF FINITE AND BOUNDARY ELEMENT METHODS IN INVESTIGATION AND PREDICTION OF LOAD-CONTROLLED NOISE OF POWER TRANSFORMERS

A recently developed calculation scheme for the computer modelling of the load-controlled noise of oil-insulated three-phase power transformers is presented. This modelling scheme allows the precise and efficient computation of the coupled electromagnetic, mechanical and acoustic fields. The equations are solved using the finite element method (FEM) as well as the boundary element method (BEM), resulting in a separation of the calculation of the winding and tank surface vibrations (using FEM) and the computation of the acoustic free-field radiation (using BEM). The complex dynamic behaviour of the loaded transformer can then be studied and, furthermore, an appropriate computer-aided design including an investigation and optimization of design parameters can be established.The validity of the computer simulations has been verified by means of appropriate measurements. Simulated and measured values for winding and tank surface vibrations as well as sound power levels of the loaded transformer are found to be in good agreement. The applicability of the calculation scheme with respect to the computer-aided design of power transformers is demonstrated by reporting two practical applications: the influence of the stiffness of winding supports and the influence of the tap changer positions.     

耦合FE/WB法在声分析中的应用

简要描叙FE法(finite element method)和WB法(wave based method)的理论背景以及耦合FE/WB法的数学基础.耦合FE/WB法利用两者的优势——FE法的广泛应用和WB法的高收敛特性,将FE模型中较大且几何简单的部分采用WB法代替.耦合模型具有相对较少的自由度.对于较高的频率还可以进行细分得到更高的计算精度,并利用模态缩减法进一步减少自由度数.数值算例结果表明,该耦合方法有潜力覆盖中频段的声分析.     

相变温度场中无网格伽辽金法的应用

简述了无单元法的基础理论,推导出相变温度场的无单元法计算公式,采用罚函数法引入了第一类边界条件,编制了相应的计算程序.通过经典相变的应用例子,和有限元计算结果及解析解的比较,说明了无单元法应用于相变温度场具有连续性好,精度高,前后处理简单等优点.