二维多流体域耦合声场的光滑有限元解法

针对声学有限元分析中四节点等参单元计算精度低,对网格质量敏感的问题,将光滑有限元法引入到多流体域耦合声场的数值分析中,提出了二维多流体域耦合声场的光滑有限元解法。该方法在Helmholtz控制方程与多流体域耦合界面的声压/质点法向速度连续条件的基础上,得到二维多流体耦合声场的离散控制方程,并采用光滑有限元的分区光滑技术将声学梯度矩阵形函数导数的域内积分转换形函数的域边界积分,避免了雅克比矩阵的计算。以管道二维多流体域耦合内声场为数值分析算例,研究结果表明,与标准有限元相比,对单元尺寸较大或扭曲严重的四边形网格模型,光滑有限元的计算精度更高。因此光滑有限元能很好地应用于大尺寸单元或扭曲严重的网格模型下二维多流体域耦合声场的预测,具有良好的工程应用前景。      

光纤—自聚焦棒—反射器耦合系统的后向耦合系数

用光线矩阵方法推导了光纤-自聚焦棒-反射器在共轴耦合情况下的后向耦合系数;分析了它与耦合系统结构参数之间的关系.用计算机模拟画出了反射器为平面镜的系统的后向耦合系数和后向耦合损耗的曲线分布,计算曲线与实验结果大致符合.     

周期孔洞区域中热力耦合问题的双尺度有限元计算

复合材料的研究中经常遇到具有周期孔洞结构的材料,由于区域的小周期性及剧烈振荡性,用传统的有限元计算方法来计算这些材料对应的问题时需要大量的计算机存储空间及计算时间.对这类材料的热力耦合问题给出了一种新型的高阶双尺度渐近解,得到了对应的均匀化常数、均匀化方程及对应的有限元算法.数值算例表明,周期单胞的局部结构对局部应力与应变有较大的影响.算法对数值模拟这类材料的力学行为是高效和可行的. 关键词： 双尺度方法 热力耦合 周期孔洞区域 有限元方法     

传递矩阵法预报时空随机激励下任意薄壳腔体内部噪声

利用结构有限元结合声有限元及边界元方法,建立了任意薄壳腔体弹性壳板振动与内外声场的耦合模型,并计算了激励力与壳板振动和内部声场之间的传递矩阵;湍流边界层脉动压力具有时空随机面激励特性,引入整体形状函数矩阵,进一步推导弹性壳板广义节点力功率谱密度函数矩阵与随机面分布激励力功率谱密度函数的关系,再利用声振耦合传递矩阵,得到弹性壳板振动和内部声场功率谱密度函数与广义节点力功率谱密度函数矩阵的关系,形成随机分布激励下任意薄壳腔体结构振动及内部声场的计算方法。以典型的内外均有声介质且一面为弹性矩形板的矩形腔声振耦合模型为例,计算了弹性壳板振动和内部声场功率谱密度函数,并与解析方法进行了比较,两者基本吻合,偏差分别为1 dB和2 dB左右。传递矩阵法不受腔体结构及其内部区域形状的制约,具有良好的适用性。      

基于Matlab的等效电子耦合原子态的矩阵计算

用专门处理矩阵的Matlab语言编程,用矩阵的思想给出了计算等效电子LS耦合原子态的计算方法.具体计算了h10电子组态的耦合原子态.     

自旋轨道耦合和电势共同调节的石墨烯中的自旋极化性质

近年来,石墨烯中电子的自旋相关输运引起了越来越多的关注.本论文应用转移矩阵的方法讨论了石墨烯中具有单个界面或者两个界面的结构中,受到自旋-轨道耦合作用和电势的共同影响下自旋相关的输运性质.对于单个界面结构,由于自旋-轨道耦合作用导致能级产生劈裂,在固定的入射能量下,电子在自旋-轨道耦合区域产生两种传播模式.在自旋-轨道耦合区域加了电势后,透射几率和模式临界角都会受到较大的影响.对于两个界面结构,粒子的透射几率不仅与入射角有关,还与自旋-轨道耦合区域的宽度和自旋进动长度有关,而电势对同自旋方向的传输几率以及自旋反转的几率都有影响,适当地选取系统的参数和电势的大小,可以控制出射的电子自旋方向,实验上可以用来设计自旋反转器或者或者自旋控制器.     

半导体瞬态问题计算方法的新进展

综述三维热传导型半导体瞬态问题计算方法的新进展.数学模型是一类由四个方程组成的非线性耦合对流-扩散偏微分方程组的初边值问题.重点研究特征分数步差分方法,修正迎风分数步差分方法,特征交替方向变网格有限元方法,区域分裂及并行计算.     

声表面波在厚金属栅阵中的耦合模参数

提出了一种研究声表面波在压电晶体厚金属栅阵中传播特性的理论方法。将有限元和声表面波在周期栅阵中的变分原理分析方法相结合,在陈东培和H.A.Haus理论基础上、用有限元分析金属短路栅对声表面波传输特性的影响,将力学负载贡献的耦合模参数用有限元矩阵表示,使其适用于声表面波在厚金属或任意形状栅条中传输情况,给出了具体理论分析方法和相应的理论表达式。最后,具体研究了几种压电晶体上金、铝或银栅阵中声表面波的传输特性,通过数值计算给出了声表面波的耦合模参数。      

随机耦合对人为反向耦合的影响

采用密度矩阵方法描述了两模反向耦合.在两模反向耦合情况下,用随机畸变的功率耦合系数(即模混合系数)对密度矩阵运动方程作了修正,并获得了修正后方程的精确解析解的表达式.     

部分浸没圆柱壳声固耦合计算的半解析法研究

部分浸没圆柱壳-流场耦合系统的声振分析是一种典型的半空间域内声固耦合问题,其振动及声学计算目前主要依赖于数值方法求解,但无论从检验数值法还是从机理上揭示其声固耦合特性,解析或半解析方法的发展都是不可或缺的.本文提出了一种半解析方法,先将声场坐标系建立在自由液面上,采用正弦三角级数来满足自由液面上的声压释放边界条件;接着基于二维Flügge薄壳理论建立了以圆柱圆心为坐标原点的壳-液耦合系统的控制方程;然后再利用Galerkin法处理声固耦合界面的速度连续条件,推导得到声压幅值与壳体位移幅值之间的关系矩阵并求解该耦合系统的振动和水下声辐射.与有限元软件Comsol进行了耦合系统自由、受迫振动和水下辐射噪声计算结的对比分析,表明本文方法准确可靠.本文的研究为解析求解弹性结构与声场部分耦合的声振问题提供了新的思路.     

Numerical simulation of the EM scattering and Doppler spectrum of a low flying target above dynamic oceanic surface by using the FEM-DDM method

The Doppler (DP) spectrum of a moving target such as a ship, an iceberg or an air-plane above dynamic oceanic surfaces[1—3] is one of the most important subjects for ra-dar oceanic surveillance, target tracking and oceanic remote sensing[4—7]. With the ad-vancement of oceanic remote sensing and radar surveillance, the experimental observa-tion and theoretical modeling of oceanic clutter have been extensively studied, e.g. by using oceanic field measurement, wave tank experiment and some stud…     

Vibro-acoustic design sensitivity analysis using the wave-based method

Conventional element-based methods, such as the finite element method (FEM) and boundary element method (BEM), require mesh refinements at higher frequencies in order to converge. Therefore, their applications are limited to low frequencies. Compared to element-based methods, the wave-based method (WBM) adopts exact solutions of the governing differential equation instead of simple polynomials to describe the dynamic response variables within the subdomains. As such, the WBM does not require a finer division of subdomains as the frequency increases in order to exhibit high computational efficiency. In this paper, the design sensitivity formulation of a semi-coupled structural-acoustic problem is implemented using the WBM. Here, the results of structural harmonic analyses are imported as the boundary conditions for the acoustic domain, which consists of multiple wave-based subdomains. The cross-sectional area of each beam element is considered as a sizing design variable. Then, the adjoint variable method (AVM) is used to efficiently compute the sensitivity. The adjoint variable is obtained from structural reanalysis using an adjoint load composed of the system matrix and an evaluation of the wave functions of each boundary. The proposed sensitivity formulation is subsequently applied to a two-dimensional (2D) vehicle model. Finally, the sensitivity results are compared to the finite difference sensitivity results, which show good agreement.     

Application of the finite element method to Monte Carlo simulations of scattering of waves by random rough surfaces: penetrable case

Abstract

The finite element method (FEM) of Monte Carlo simulations of random rough surface scattering is extended to penetrable rough surface scattering. The attraction of the method is the banded nature of the resulting matrix equation. The method yields a system of linear algebraic equations which is solved by a direct sparse symmetric matrix inversion. Convergence and accuracy of the method is demonstrated and established by varying various input parameters such as the number of evanescent waves, the number of sampling points and the surface lengths. Results with incident plane wave TE polarization are presented for both the mean reflected scattered intensity and the mean transmitted scattered intensity as a function of surface parameters such as RMS surface heights and correlation lengths. The numerical results are compared against the tapered wave integral equation (TWIE) method. The results of a tapered wave solution of the integral equation averaging over many realizations are in good numerical agreement with FEM if large surface lengths are used in the integral equation method. It is found that a large surface length is required in the TWIE method to have a narrow incident angular spectlum to accurateiy predict the transmitted scattered intensity, whereas a relatively small surface length is sufficient in the FEM. The total CPU time and memory storage requirements for the FEM are much less than that of the TWIE method for eases when the number of horizontal sampling points is much larger than the number of vertical sampling points in the region of discretization. The percentage error in conservation of energy for the FEM is shown to be less than 0.4% for all the examples presented. The total CPU time, memory storage requirements and the percentage error comparisons between the FEM and the TWIE are presented.     

Application of the finite element method to Monte Carlo simulations of scattering of waves by random rough surfaces: penetrable case

The finite element method (FEM) of Monte Carlo simulations of random rough surface scattering is extended to penetrable rough surface scattering. The attraction of the method is the banded nature of the resulting matrix equation. The method yields a system of linear algebraic equations which is solved by a direct sparse symmetric matrix inversion. Convergence and accuracy of the method is demonstrated and established by varying various input parameters such as the number of evanescent waves, the number of sampling points and the surface lengths. Results with incident plane wave TE polarization are presented for both the mean reflected scattered intensity and the mean transmitted scattered intensity as a function of surface parameters such as RMS surface heights and correlation lengths. The numerical results are compared against the tapered wave integral equation (TWIE) method. The results of a tapered wave solution of the integral equation averaging over many realizations are in good numerical agreement with FEM if large surface lengths are used in the integral equation method. It is found that a large surface length is required in the TWIE method to have a narrow incident angular spectlum to accurateiy predict the transmitted scattered intensity, whereas a relatively small surface length is sufficient in the FEM. The total CPU time and memory storage requirements for the FEM are much less than that of the TWIE method for eases when the number of horizontal sampling points is much larger than the number of vertical sampling points in the region of discretization. The percentage error in conservation of energy for the FEM is shown to be less than 0.4% for all the examples presented. The total CPU time, memory storage requirements and the percentage error comparisons between the FEM and the TWIE are presented.     

二维非均匀介质中大地电磁响应的计算

在二维埋均匀介质中,将大地电磁问题可看作电磁波在有耗开放波导中的传播问题,借用研究波导问题的数值模式匹配法予以解决,在计算Ex型问题时,使用Hermite基函数和非均匀无素;在计算Hx型问题时,使用变型Hermite基函数,并与有限元法进行了比较。     

Study on Combined Method Based on 3-D ESPI

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Study on Combined Method Based on 3-D ESPI

The finite element method (FEM),whether the calculation is accurate or not,depends closely on object boundary condition.If the three dimensional displacement of the object obtained in experiment is regarded as its boundary condition,a new method combining the results of experiment and calculation,called combined method (CM),is formed.The combined method possess advantages of experiment and calculation.It can correct calculation and improve the accuracy of FEM.Accordingly it has more practicability.In this paper,the three dimensional displacement fields of a typical beam loaded at three points are tested by using 3-D electric speckle pattern interferometry (ESPI).Using the experimental results as boundary condition the whole three-dimensional displacement fields can be calculated by FEM.The beam′s three-dimensional displacement fields obtained by FEM agree very well with those obtained by experiment.This proves that the combined method is effective and practicable.     

Improved transmission conditions for a one-dimensional domain decomposition method applied to the solution of the Helmholtz equation

The scattering problem of a time-harmonic electromagnetic wave from a perfect electric conductor (PEC) coated with materials is considered, and solved by coupling a finite element method with an integral equation prescribed on the outer boundary of the computational domain. To reduce the numerical complexity, a one-dimensional domain decomposition method (DDM) is employed: the computational domain is partitioned into concentric subdomains (SDs), and Robin transmission conditions (TCs) are prescribed on the interfaces. For some configurations and/or materials, the convergence of the corresponding DDM algorithm happens to be slow. A possible remedy is to enhance the efficiency of the TCs by approximating the exact ones more accurately. To this end, we first consider the simplified 2D problem of a circular PEC cylinder with an homogeneous coating and up to four SDs with circular interfaces, thus allowing to obtain the exact TCs in closed-form. Approximate local or non-local TCs are derived from these exact ones, and numerical examples demonstrate their superiority over the standard Robin TCs. Then, the case of an elliptical PEC cylinder with one interface in free-space is investigated. Also, the issues pertaining to the uniqueness of the solutions and convergence of the algorithm are addressed.     

Scattering of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces – study with the curvilinear coordinate method

We present a method giving the bi-static scattering coefficient of two-dimensional (2-D) perfectly conducting random rough surface illuminated by a plane wave. The theory is based on Maxwell's equations written in a nonorthogonal coordinate system. This method leads to an eigenvalue system. The scattered field is expanded as a linear combination of eigensolutions satisfying the outgoing wave condition. The boundary conditions allow the scattering amplitudes to be determined. The Monte Carlo technique is applied and the bi-static scattering coefficient is estimated by averaging the scattering amplitudes over several realizations. The random surface is represented by a Gaussian stochastic process. Results are compared to published numerical and experimental data. Comparisons are conclusive.     

Scattering of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces - study with the curvilinear coordinate method

We present a method giving the bi-static scattering coefficient of two-dimensional (2-D) perfectly conducting random rough surface illuminated by a plane wave. The theory is based on Maxwell's equations written in a nonorthogonal coordinate system. This method leads to an eigenvalue system. The scattered field is expanded as a linear combination of eigensolutions satisfying the outgoing wave condition. The boundary conditions allow the scattering amplitudes to be determined. The Monte Carlo technique is applied and the bi-static scattering coefficient is estimated by averaging the scattering amplitudes over several realizations. The random surface is represented by a Gaussian stochastic process. Results are compared to published numerical and experimental data. Comparisons are conclusive.