基于有限元的平面光波导粘接热应力分析

基于有限元理论对阵列光纤和波导芯片粘接情况进行了建模与仿真,分析了在温度变化下不同粘接区域厚度的热应力和微位移的产生和分布,结果表明粘接界面的边缘区域对温度变化最敏感.根据光弹效应定性分析了粘接区域的应力双折射,并利用光束传播法计算了由此微位移所导致的光功率损耗,结果表明若以附加损耗小于0.15 dB的标准考察,则必须要求粘胶厚度的理论值在16 μm以内.总结了温度变化和在相同条件下不同粘胶厚度对平面光波导封装性能的影响规律.     

A Method of Lines Based on Immersed Finite Elements for Parabolic Moving Interface Problems

This article extends the finite element method of lines to a parabolic initial boundary value problem whose diffusion coefficient is discontinuous across an interface that changes with respect to time. The method presented here uses immersed finite element (IFE) functions for the discretization in spatial variables that can be carried out over a fixed mesh (such as a Cartesian mesh if desired), and this feature makes it possible to reduce the parabolic equation to a system of ordinary differential equations (ODE) through the usual semi-discretization procedure. Therefore, with a suitable choice of the ODE solver, this method can reliably and efficiently solve a parabolic moving interface problem over a fixed structured (Cartesian) mesh. Numerical examples are presented to demonstrate features of this new method.     

冲击动力学中离散元与有限元相结合的计算方法研究

 阐述了一种离散元与有限元法相结合的计算方法,编制了可应用于细观模拟的二维程序,对受冲击载荷作用的均匀材料和非均匀材料的响应特征进行了计算,并对数值模拟进行了验证。计算结果与理论值较吻合,验证了方法的可行性。     

离散元与有限元结合的多尺度方法及其应用

在深入研究复杂结构和非均质材料冲击响应和破坏机理的过程中,往往遇到多尺度计算问题.提出并建立起离散元与有限元结合的多尺度方法,该方法采用离散元对感兴趣的局部进行细观尺度的模拟,利用有限元进行宏观的模拟,从而节约了计算时间.采用一种特殊的过渡层衔接离散元区和有限元区.将这一方法应用于激光辐照下预应力铝板的破坏响应,并将得到的模拟结果与实验进行了比较.     

On the Electric Field Lines of the Dominant Mode in Millimetric V-Groove Guide by Finite Element Method

In this paper, the electric field lines of the dominant mode in a closed V-groove guide as well as an open one are analysed by finite element method. The results show that the electric field lines are not parallel to the parallel plate region, but perpendicular to them. Since the attenuation increase with increasing frequency when the electric field lines are perpendicular to the mental walls, the V-groove is not suitable to be used in millimeter and submillimeter wavebands, and it is can't be regarded as low-loss wave guiding structures.     

求解薛定锷方程的有限元离散格点表象

提出了利用映射函数来调节有限元离散格点表象的格点分布,从而提高其数值效率．为了测试该新方法的数值效率,将其用于氢原子中电子的本征态和本征能量以及具有长程势的Cs₂分子三重态的振动能级的求解,并与最初的有限元离散格点表象方法作了比较．计算结果表明：利用格点映射的方法可以显著提高限元离散格点表象的数值效率     

辐射传输方程的三阶球谐展开(P3)近似的有限元法求解

从辐射传输方程出发,应用球谐函数方法对辐射率进行多项式展开,并利用球谐函数的正交性和递推性,在二维笛卡儿坐标下,导出了三阶展开的球谐函数微分方程组（P3近似）,改进了以往成像文献中忽略各项异性因子的P3近似,并用有限元方法对二维圆域均匀和非均匀两种情况做了数值模拟.与漫射近似模型相比较,P3近似能更准确地描述光源附近及吸收较强情况下边界的光辐射分布情况.     

Si2N2O基体铌酸锂调制器有限元法研究

提出一种新型基于Si2N2O基体的LiNbO3行波调制器,利用有限元方法对该调制器进行数值分析并获得调制器的优化结构尺寸.该新型调制器带宽达到120 GHz,半波电压为3.5 V,特性阻抗为50.2 Ω.结果表明该调制器具有大的调制带宽和良好的阻抗匹配,在未来光通信中具有很好的应用前景.     

On Single-Mode Bandwidth in Rectangular-Groove Guide by Finite Element Method

The single-mode bandwidth in rectangular-groove guides with different dimensions has been studied by finite element method. The actual single-mode bandwidth in a rectangular-groove guide is the same with a rectangular guide with the similiar dimensions. The dominant single-mode transmission in a rectangular-groove guide at millimetric waveband by adjusting the guide dimensions can only be an approximate one.     

Discrete Maximum Principle Based on Repair Technique for Finite Element Scheme of Anisotropic Diffusion Problems

In this paper, we construct a global repair technique for the finite element scheme of anisotropic diffusion equations to enforce the repaired solutions satisfying the discrete maximum principle. It is an extension of the existing local repair technique. Both of the repair techniques preserve the total energy and are easy to be implemented. The numerical experiments show that these repair techniques do not destroy the accuracy of the finite element scheme, and the computational cost of the global repair technique is lower than the local repair technique when the diffusion tensors are highly anisotropic.     

On the Dominant Mode in Closed Trapezoidal-Groove Guide by Finite Element Method

The structure of closed trapezoidal-groove guide is similiar to that of open one, but it can be used to prevent energy from leaking out of the guide. In this paper, the propagation characteristics of dominant mode in closed trapezoidal-groove guide are analysed by using finite element method and the results are discussed.     

Field Patterns in Double Circular-Groove Guide by Finite Element Method

The electromagnetic power coupling in symmetrical and asymmetrical double circular-groove guides have been analyzed by finite element method (FEM) in this paper. The electrical field patterns of the dominant mode and the first higher-order TE mode have been presented. The electromagnetic field of the dominant mode distributes with a concentration in the two grooves and the region between grooves as well for symmetrical double circular-groove guide, while it distributes with a concentration in the groove with larger radius for the asymmetrical double circular-groove guide. The electrical field patterns of the first higher-order TE mode in symmetrical and asymmetrical double circular-groove guide are also presented. The figures in this paper have important values in design of circular-groove guide power coupler for millimeter wave applications.     

A Fast Finite Element Analysis of Millimeter Wave Waveguide Filters

The multifrontal method is applied for solving a large system of linear equations resulting from the use of edge-based finite element method (FEM). The finite element method combined with the perfectly matched layers (PML) is given for simulation of microwave filters and the algorithm of multifrontal method is described in detail. The reflection and insertion losses of millimeter wave filter are analyzed as the examples and the obtained results are compared with those obtained from literature. In order to demonstrate the efficiency of the multifrontal method, the computational time is compared with that of both symmetric successive overrelaxation (SSOR) preconditioned conjugate gradient (PCG) and conjugate gradient methods (CG) for the thick-iris waveguide bandpass filer.     

Field Patterns in Asymmetrical Double Groove Guide by Finite Element Method

The electromagnetic power coupling in asymmetrical double-groove guide is analyzed by finite element method (FEM) in this paper. The electrical field patterns of the dominant mode and the first higher-order TE mode have been presented. The electromagnetic field of the dominant mode is distributed with a concentration of energy in the wide groove region, while the electromagnetic field of the first higher-order TE mode is distributed with a concentration of energy in the narrow groove region. The results in this paper have important values in design of groove guide power coupler for millimeter wave applications.     

Design of a Rectangular to Circular Groove Waveguide Transition by Finite Element Method

A rectangular to circular groove waveguide transition is described in millimeter-wave band. The transition maintains a constant cutoff wavelength. Using the Finite Element Method, the size of the variable cross-section throughout the transition are calculated and the transition is designed.     

Application of SSOR Preconditioning Technique to Method of Lines for Millimeter Wave Scattering

In this paper, symmetric successive overrelaxation (SSOR) preconditioned CG technique are introduced into method of lines (MOL) to further enhance the computational efficiency of this semi-analytic method. Millimeter wave scattering by an infinite plane metallic grating is used as the examples to describe its implementation, whose analysis usually needs fast algorithms because of electrically large dimension. For arbitrary incident wave, Helmholz equation and boundary condition are used to calculate the impedance matrix and then to obtain reduced current-voltage linear matrix equation in spatial domain. An effective symmetric successive overrelaxation preconditioned conjugate gradient iterative method, SSOR-PCG, is chosen to solve this matrix equation. With SSOR as the preconditioner as well as its efficient implementing in CG algorithm, PCG method can converge to accurate solution in much fewer iteration steps.     

变形镜像差拟合能力的有限元仿真

为了研究变形镜对于Zernike多项式像差模式的拟合能力, 利用有限元仿真方法, 建立了两种不同单元排布方式的变形镜有限元模型. 通过给促动器施加理论位移, 进行了仿真分析. 结果指出了不同的促动器排布方式与像差拟合能力之间的关系, 同时表明57点促动器密布的排列方式已经能校正像差到λ/20甚至更小, 验证了促动器对变形镜“印透效应”等的影响.     

间断有限元方法求解一维非平衡辐射扩散方程

研究一维非平衡辐射扩散方程的数值方法.通过求解间断系数热传导方程的广义黎曼问题,得到一种带加权数值流量,基于该数值流量构造了一类新型的间断有限元方法.在时间离散上采用向后Euler方法,形成的非线性方程组采用Picard迭代求解.数值试验表明该方法具有捕捉大梯度的能力,而且能适应扩散系数间断的情形.     

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.     

Moving Finite Element Methods for a System of Semi-Linear Fractional Diffusion Equations

This paper studies a system of semi-linear fractional diffusion equations which arise in competitive predator-prey models by replacing the second-order derivatives in the spatial variables with fractional derivatives of order less than two. Moving finite element methods are proposed to solve the system of fractional diffusion equations and the convergence rates of the methods are proved. Numerical examples are carried out to confirm the theoretical findings. Some applications in anomalous diffusive Lotka-Volterra and Michaelis-Menten-Holling predator-prey models are studied.