Multisymplectic Structure－Preserving in Simple Finite Element Method in High Dimensional Case

In this paper, we study a finite element scheme of some semi-linear elliptic boundary value problems in high-dhnensjonal space. With uniform mesh, we find that, the numerical scheme derived from finite element method can keep a preserved multisymplectic structure.     

Multisymplectic Structure-Preserving in Simple Finite Element Method in High Dimensional Case

In this paper, we study a finite element scheme of some semi-linear elliptic boundary value problems inhigh-dimensional space. With uniform mesh, we find that, the numerical scheme derived from finite element method cankeep a preserved multisymplectic structure.     

A fuzzy finite element procedure for the calculation of uncertain frequency response functions of damped structures: Part 2—Numerical case studies

This work introduces a numerical algorithm to calculate frequency response functions of damped finite element models with fuzzy uncertain parameters. Part 1 of this paper focusses on the numerical procedure for the solution of the underlying interval finite element problem, based on the undamped procedure and the principle of Rayleigh damping. Part 2 of this paper illustrates the applicability of the methodology through four case studies. The concepts of the interval and the fuzzy finite element frequency response function analysis are illustrated for different types of uncertainties. The obtained results are compared with the results of Monte Carlo simulations.     

多孔复合介质周期结构热传导和质扩散问题的多尺度数值方法

本文针对一类复杂的多孔复合介质的热传导和质扩散问题,给出具体的多尺度渐近展开公式,并在此基础上设计了有限元算法格式,它是宏观和细观相结合的数值方法。理论分析和数值实验均表明：多尺度数值方法对求解多孔复合介质周期结构的热传导和质扩散问题是可行的和有效的。     

Application of the FEM and the BEM to compute the field of a transducer mounted in a rigid baffle (3D case)

A three-dimensional finite element model has been developed which allows the harmonic analysis of a piezoelectric structure mounted on a rigid baffle and radiating into water. The solution of this problem consists of coupling a finite element method to a boundary element method. The first one enables the modelling of the vibrating structure and the second one the modelling of propagating waves in the semi-infinite fluid medium surrounding the structure. In this way, the near-field and the far-field pressures are calculated as well as the displacement field of the piezoelectric structure taking into account the acoustical interaction. Numerical and experimental results are provided which validate the numerical procedure. The good agreement obtained indicates that this three-dimensional model is a very useful tool to optimise the design of transducer arrays used in medical imaging.     

孔耦合自由电子激光振荡器的数值模拟方法

针对孔耦合波导自由电子激光振荡器腔内光场横向特性,应用有限元法于慢变光场方程,并对输出腔镜上孔耦合过程加以较准确的描述,而后通过对数值结果的分析比较,说明这一模拟方法较好地描述了孔耦合引起的腔内光场横向结构的变化发展特性,改善了模拟结果。     

Finite Difference/Element Method for a Two-Dimensional Modified Fractional Diffusion Equation

We present the finite difference/element method for a two-dimensional modified fractional diffusion equation. The analysis is carried out first for the time semi-discrete scheme, and then for the full discrete scheme. The time discretization is based on the $L1$-approximation for the fractional derivative terms and the second-order backward differentiation formula for the classical first order derivative term. We use finite element method for the spatial approximation in full discrete scheme. We show that both the semi-discrete and full discrete schemes are unconditionally stable and convergent. Moreover, the optimal convergence rate is obtained. Finally, some numerical examples are tested in the case of one and two space dimensions and the numerical results confirm our theoretical analysis.     

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     

三维材料微结构设计与数值模拟

为了研究材料细观尺度的力学性能与失效行为,达到对材料微结构的“性能导向型”设计与性能预测的目的,通过程序设计结合有限元数值模拟的方法实现多元多相异质体材料微观组织结构的计算机仿真、材料微结构的细观力学计算与虚拟失效分析.以材料微观组织结构计算机仿真软件ProDesign构造的多晶体材料与多晶体基复合材料微结构的代表性体积单元为基础,基于对商业有限元软件ABAQUS的二次开发,实现对材料微结构细观力学的数值计算,并根据数值模拟结果预测微结构的材料性能,识别“材料结构弱点”,评估异质体材料微结构内微裂纹的启裂 关键词： 材料微结构 数值模拟 各向异性 虚拟失效     

A New Finite Volume Element Formulation for the Non-Stationary Navier-Stokes Equations

A semi-discrete scheme about time for the non-stationary Navier-Stokes equations is presented firstly, then a new fully discrete finite volume element (FVE) formulation based on macroelement is directly established from the semi-discrete scheme about time. And the error estimates for the fully discrete FVE solutions are derived by means of the technique of the standard finite element method. It is shown by numerical experiments that the numerical results are consistent with theoretical conclusions. Moreover, it is shown that the FVE method is feasible and efficient for finding the numerical solutions of the non-stationary Navier-Stokes equations and it is one of the most effective numerical methods among the FVE formulation, the finite element formulation, and the finite difference scheme.     

Coupled fluid–structure solver: The case of shock wave impact on monolithic and composite material plates

An unstructured adaptive mesh flow solver, a finite element structure solver and a moving mesh algorithm were implemented in the numerical simulation of the interaction between a shock wave and a structure. In the past, this interaction is mostly considered as one-way in the sense that the shock causes a transient load on the structure while it is reflected uneffected by the impact. A fully coupled approach was implemented in the present work which can account for the effects associated with a mutual interaction. This approach included a compressible flow Eulerian solver of second order accuracy in finite volume formulation for the fluid and a Langargian solver in finite element formulation for the solid structure. A novel implementation of advancing front moving mesh algorithm was made possible with the introduction of a flexible and efficient quad-edge data structure. Adaptive mesh refinement was introduced into the flow solver for improved accuracy as well. Numerical results are further validated by theoretical analysis, experimental data and results from other numerical simulations. Grid dependency study was performed and results showed that the physical phenomena and quantities were independent of the numerical grid chosen in the simulations. The results illuminated complicated flow phenomena and structure vibration patterns, which in order to be detected experimentally require capabilities beyond those of the current experimental techniques. The numerical simulations also successfully modelled the aero-acoustic damping effects on the structure, which do not exist in previous numerical models. Further analysis of the results showed that the mutual interaction is not linear and that the non-linearity arises because the wave propagation in the fluid is not linear and it cascades a non-linear and non-uniform loading on the plate. Non-linearity intensifies when the plate is vibrating at high frequency while the wave propagation speed is low.     

三维电磁扩散场数值模拟及磁化效应的影响

采用矢量有限元法实现了三维电磁扩散场数值模拟,并成功将其应用在大地电磁的正演研究中.为灵活精确地拟合起伏地形和地下不规则构造,采用由不规则四面体单元组成的非结构化网格,可根据模型设计的需要调整网格的大小.引入了基于二次场理论,将解析的一次场从总场中扣除,直接计算二次场,使得误差仅局限于相对较小的二次场,以提高总场计算精度.常规的节点有限元法不满足电性分界面上法向电场不连续和无源区单元内电流密度无散,违反麦克斯韦方程组.为克服节点有限元法的弊端,使用矢量有限元法求解基于二次电场的偏微分方程.另外,在算法设计中,考虑了磁导率参数的变化,可以模拟磁导率不均匀的模型.通过与COMMEMI模型已发表的结果对比,证明了本文算法的正确性和精确性.为突显非结构网格优势,计算了椭球异常体模型和任意地形模型的MT响应,并详细讨论了地形和磁化效应对三维数值模拟结果的影响.     

A finite element scheme to study the nonlinear optical response of a finite grating without and with defect

We present a simple numerical scheme based on the finite element method (FEM) using transparent-influx boundary conditions to study the nonlinear optical response of a finite one-dimensional grating with Kerr medium. Restricting first to the linear case, we improve the standard FEM to get a fourth order accurate scheme maintaining a symmetric-tridiagonal structure of the finite element matrix. For the full nonlinear equation, we implement the improved FEM for the linear part and a standard FEM for the nonlinear part. The resulting nonlinear system of equations is solved using a weighted-averaged fixed-point iterative method combined with a continuation method. To illustrate the method, we study a periodic structure without and with defect and show that the method has no problem with large nonlinear effect. The method is also found to be able to show the optical bistability behavior of the ideal and the defect structure as a function of either the frequency or the intensity of the input light. The bistability of the ideal periodic structure can be obtained by tuning the frequency to a value close to the bottom or top linear band-edge while that of the defect structure can be produced using a frequency near the defect mode or near the bottom of the linear band-edge. The threshold value can be reduced by increasing the number of layer periods. We found that the threshold needed for the defect structure is much lower then that for a strictly periodic structure of the same length.     

A priori mesh quality metric error analysis applied to a high-order finite element method

Characterization of computational mesh’s quality prior to performing a numerical simulation is an important step in insuring that the result is valid. A highly distorted mesh can result in significant errors. It is therefore desirable to predict solution accuracy on a given mesh. The HiFi/SEL high-order finite element code is used to study the effects of various mesh distortions on solution quality of known analytic problems for spatial discretizations with different order of finite elements. The measured global error norms are compared to several mesh quality metrics by independently varying both the degree of the distortions and the order of the finite elements. It is found that the spatial spectral convergence rates are preserved for all considered distortion types, while the total error increases with the degree of distortion. For each distortion type, correlations between the measured solution error and the different mesh metrics are quantified, identifying the most appropriate overall mesh metric. The results show promise for future a priori computational mesh quality determination and improvement.     

Finite element method for modeling radiative transfer in semitransparent graded index cylindrical medium

Both Galerkin finite element method (GFEM) and least squares finite element method (LSFEM) are developed and their performances are compared for solving the radiative transfer equation of graded index medium in cylindrical coordinate system (RTEGC). The angular redistribution term of the RTEGC is discretized by finite difference approach and after angular discretization the RTEGC is formulated into a discrete-ordinates form, which is then discretized based on Galerkin or least squares finite element approach. To overcome the RTEGC-led numerical singularity at the origin of cylindrical coordinate system, a pole condition is proposed as a special mathematical boundary condition. Compared with the GFEM, the LSFEM has very good numerical properties and can effectively mitigate the nonphysical oscillation appeared in the GFEM solutions. Various problems of both axisymmetry and nonaxisymmetry, and with medium of uniform refractive index distribution or graded refractive index distribution are tested. The results show that both the finite element approaches have good accuracy to predict the radiative heat transfer in semitransparent graded index cylindrical medium, while the LSFEM has better numerical stability.     

吸声材料对水下小平台上矢量传感器声学特性的影响研究

本文围绕粘贴黏弹性吸声材料方法对水下小平台上安装矢量传感器的指向性和测向的影响展开理论分析和实验研究.首先建立了吸声材料和平台结构组成的复合层结构的数学模型,对声波经过复合层结构的声学特性进行了分析,在此基础上利用有限元耦合边界元法对粘贴吸声材料前后的水下小平台上的矢量传感器的声学特性进行研究.通过理论计算和数值分析研究了吸声材料对矢量传感器的各通道的指向性的影响,并计算了覆盖吸声材料前后矢量传感器的测向精度.水池实验验证了分析结果的正确性.     

Selectivity of seismic electric signal (SES) of the 2000 Izu earthquake swarm: a 3D FEM numerical simulation model

Although seismic electric signal (SES) has been used for short-term prediction of earthquakes, selectivity of SES still remains as one of the mysterious features. As a case study, we made a numerical simulation based on a 3D finite element method (FEM) on the selectivity of SES observed in the case of the 2000 Izu earthquake swarm. Our numerical results indicated that the existence of conductive channel under Niijima island could explain the reported SES selectivity.     

A Finite Volume Method for the Approximation of Diffusion Operators on Distorted Meshes

A new finite volume method is presented for discretizing general linear or nonlinear elliptic second-order partial-differential equations with mixed boundary conditions. The advantage of this method is that arbitrary distorted meshes can be used without the numerical results being altered. The resulting algorithm has more unknowns than standard methods like finite difference or finite element methods. However, the matrices that need to be inverted are positive definite, so the most powerful linear solvers can be applied. The method has been tested on a few elliptic and parabolic equations, either linear, as in the case of the standard heat diffusion equation, or nonlinear, as in the case of the radiation diffusion equation and the resistive diffusion equation with Hall term.     

Time-domain analyses of acoustics-structure interactions for piezoelectric transducers.

Piezoelectric transducers coupled with a surrounding medium are analyzed in time domain using the coupled finite element and boundary element method. Three-dimensional solid elements are employed to model the piezoelectric transducer, while the surrounding medium is described by the boundary integral equation and the boundary of the medium is modeled by two-dimensional spatial elements. Verification studies were conducted to evaluate the accuracy and convergence of the present numerical algorithm and they show that the present numerical solutions agree well with the analytical ones. The influence of the surrounding medium on the acoustic field is studied. The interaction between the structure and surrounding medium affects the structure dynamic performances and acoustic pressure distributions significantly. However, in the present study we show that the radiation directivity is insignificantly influenced by the surrounding medium.