一类非线性Scllr(o)dillger方程的差分/Legendre谱元法

考察一类带幂次非线性项的Schrodinger方程的Dirichlet初边值问题,提出了一个有效的计算格式,其中时间方向上应用了一种守恒的二阶差分隐格式,空间方向上采用Legendre谱元法.对于时间半离散格式,证明了该格式具有能量守恒性质,并给出了L2误差估计,对于全离散格式,应用不动点原理证明了数值解的存在唯一性,并给出了L2误差估计.最后,通过数值试验验证了结果的可信性.     

波动方程的边界单元法

本文从三维波动方程的Kirchhoff积分公式出发,首先经离散化给出无限均匀介质中的边界单元法公式.其后,在引入了波在不同介质面和自由面上的反射、折射系数以后,给出了三维波动方程在分区均匀介质中的边界单元法公式.     

Taylor-Couette流稳定性的谱方法研究

该文根据ｓｔｏｋｅｓ算子特征函数,利用谱方法研究了由轴对称Ｔａｙｌｏｒ Ｃｏｕｅｔｔｅ流导出的多模态方程．给出了三模态方程平衡点存在的条件,证明了它的吸引子的存在性,并给出其Ｈａｕｓ ｄｏｒｆｆ维数的上界的估计．     

Dynamic analysis of functionally graded nanocomposite beams reinforced by randomly oriented carbon nanotube under the action of moving load

This work deals with a study of the vibrational properties of functionally graded nanocomposite beams reinforced by randomly oriented straight single-walled carbon nanotubes (SWCNTs) under the actions of moving load. Timoshenko and Euler-Bernoulli beam theories are used to evaluate dynamic characteristics of the beam. The Eshelby-Mori-Tanaka approach based on an equivalent fiber is used to investigate the material properties of the beam. An embedded carbon nanotube in a polymer matrix and its surrounding inter-phase is replaced with an equivalent fiber for predicting the mechanical properties of the carbon nanotube/polymer composite. The primary contribution of the present work deals with the global elastic properties of nano-structured composite beams. The system of equations of motion is derived by using Hamilton’s principle under the assumptions of the Timoshenko beam theory. The finite element method is employed to discretize the model and obtain a numerical approximation of the motion equation. In order to evaluate time response of the system, Newmark method is also used. Numerical results are presented in both tabular and graphical forms to figure out the effects of various material distributions, carbon nanotube orientations, velocity of the moving load, shear deformation, slenderness ratios and boundary conditions on the dynamic characteristics of the beam. The results show that the above mentioned effects play very important role on the dynamic behavior of the beam and it is believed that new results are presented for dynamics of FG nano-structure beams under moving loads which are of interest to the scientific and engineering community in the area of FGM nano-structures.     

THE LARGE TIME CONVERGENCE OF SPECTRAL METHOD FOR GENERALIZED KURAMOTO-SIVASHINSKY EQUATION (Ⅱ)

1.IntroductionInthepaper[1],westudedthegeneralizedKuramotrySivashinskyequationWeProvedtheexistenceanduniquenessofglobalsolutionforperiodicinitialproblemandgavethelargetimeerrorestimationforthesolutionofcontinuousspectralmethod.Theaimofthispaperistostudyfullydiscretespectralmethodandthelongtimebehaviorofthesolutionofthissystem.In61wegiventhelargetimeerrorestimationforfullydiscretesolutionofspectralmethod.In52weprove-theexistenceofapproximateattractorsAN,4anding3weprovetheconvergenceofapproal…     

The Concept of Dividing Lines/Surfaces for the Finite Difference Element Method (FDEM)

The FDEM (Finite Difference Element Method) is a black‐box solver for the solution of nonlinear systems of elliptic and parabolic PDEs [1]. We use a FDM of arbitrary consistency order on an unstructured FEM mesh. We compute a reliable error estimate which we also use for an automatic consistency order control and mesh refinement. By dividing lines (2‐D) or dividing surfaces (3‐D) we extend this method for the uniform solution over coupled domains.     

对流扩散方程的间断时空有限元方法的误差估计

研究了一类线性对流扩散方程的间断时空有限元方法,即空间连续,时间允许间断的时空有限元方法.将有限元方法和有限差分方法相结合,在每一时间层上充分利用Lagrange插值多项式在Radau点处的特性,给出了有限元解的最优阶L∞(L2)模误差估计.     

Optimal Shape Design for Metal Forming Problems by the Finite Element Method

In this work, a method for calculation of the optimal shapes of axisymmetrical converging dies by the finite element method is presented. The shape optimization problem considered in this paper is to find the best shape of the die such that the flow rate will be uniform at the die exit.The optimization problem is to minimize an objective function by varying a part of boundary (ie: the shape of die) subject to constraints imposed by the metal forming problem. In this method, the B-spline functions allow us to determine the shape of the die, using its control points as design variables. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of Piezoelectric Smart Lightweight Structures by the Finite Element Method for Acoustic Control

Piezoelectric patches are widely used as distributed actuators and sensors for active vibration control. Active control of sound in this way is mainly interesting in the low frequency range, where passive methods are less effective. To simulate such electromechanical‐acoustical systems a virtual overall model based on the FEM is presented in the paper. Different approaches for model reduction with respect to controller design purposes are discussed. As a simple test example the numerical model of an acoustic box is studied. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Study of Multiple Solutions for the Navier-Stokes Equations by a Finite Element Method

In this paper, a finite element method is proposed to investigate multiple solutions of the Navier-Stokes equations for an unsteady, laminar, incompressible flow in a porous expanding channel. Dual or triple solutions for the fixed values of the wall suction Reynolds number $R$ and the expansion ratio $α$ are obtained numerically. The computed multiple solutions for the symmetric flow are validated by comparing them with approximate analytic solutions obtained by the similarity transformation and homotopy analysis method. Unlike previous works, our method deals with the Navier-Stokes equations directly and thus has no similarity and other restrictions as in previous works. Finally we use the method to study multiple solutions for three cases of the asymmetric flow (which has not been studied before using the similarity-type techniques).     

手性障碍电磁散射的PML有限元计算

该文建立了手性障碍电磁散射问题的二维模型, 给出问题的有限元分析, 并利用结合PML(perfectly matched layers)技术的有限元法进行数值模拟.     

自适应有限元方法在凹角域线性椭圆方程的应用(续)

作为序列文章自适应有限元方法在凹角域线性椭圆方程的应用的第三篇,在本文我们将给出并详细论证一个重要结论即 |?(u(x)-U(x))|≤Ch(x)|x|^β-2,|x|≥C′h且进一步分析说明在本序列文章的第一部分和地二部分得出方法都是以此为基础作出的。     

Error Estimates for the Solution of the Radial Schr?dinger Equation by the Rayleigh--Ritz Finite Element Method

Approximate eigenvalues and eigenfunctions are obtained forthe radial Schr?dinger equation by applying the Rayleigh—Ritzmethod to a function space consisting of polynomial splinesof odd degree. Computable a posteriori error estimates for theeigenfunction error estimates are obtained. The sharpness ofthese estimates is illustrated for the harmonic oscillator andWoods—Saxon potentials, using both cubic splines and piecewisecubic Hermite polynomials.     

基于结构方程模型的当代大学生毕业去向选择行为研究

大学生作为未来社会劳动力的重要组成部分,其毕业后的去向选择一直是社会各界广泛关注的热点.近年来,对大学生毕业去向选择问题的研究愈来愈多,其中不乏出现"考研热"、"考公务员热"、"出国热"等选择行为.大学生对毕业去向选择是否盲目?其选择行为又受到哪些因素的影响?为此,对江西省部分高校大学生择业意向进行了问卷调查,利用结构方程模型,对毕业生择业行为的影响因素及其路径给出了分析,并就当前的教育、就业与创业等存在的不足之处提出改进对策与建议.     

利用Tanh方法产生的(2+1)和(3+1)维非线性可积方程的精确解

主要利用Tanh函数方法,对两个高维五阶非线性可积方程进行了讨论,通过行波约化,分别将(2+1)和(3+1)维非线性可积方程转化为常微分方程.结合Riccati方程的性质,分别得到关于若干参变量的代数系统,借助于Mathematica软件符号运算功能,最终得到了上述两个高维方程的精确解.     

多变量样条元法分析弹性地基板的弯曲,振动与稳定问题

本文应用双三次乘积型二元B样条函数来构造弹性地基板的位移、弯矩和扭矩等多种场函数，由混合变分原理导出多变量样条无法方程．文中，对弹性地基板的弯曲、振动与稳定问题作了分析与计算．由于，本文方法设定了各自独立的场函数，因此，所算得的场未知量如位移、弯矩和扭矩值的精度均比较高。     

Quasirecognizability by the Set of Element Orders for Groups 3 D 4(q), for q Even

It is proved that if G is a finite group with an element order set as in the simple group ³D₄(q), where q is even, then the commutant of G/F(G) is isomorphic to ³D₄(q) and the factor group G/G′ is a cyclic {2, 3}-group. __________ Translated from Algebra i Logika, Vol. 45, No. 1, pp. 3–19, January–February, 2006.