A2B分子反映系统经典轨迹计算的有限元方法

本文利用常微分方程的连续有限元法计算了A2B模型的分子的经典轨迹和能量误差，将计算延长到10^-sS，并与辛算法进行了比较．结果表明，在微观反映动力学研究所考虑的时间范围内，有限元法的结果与理论分析一致，能较长时间保持能量守恒和系统整体结构，并在数值计算上探讨了守恒性和近似程度，结果与理论相吻合。     

考虑摩擦接触时简谐波透过微缝隙的传播

研究了简谐波透过微缝隙的传播问题．考虑界面摩擦接触,利用Fourier分析技术和半空间解修正法,将边界非线性波动问题简化为一组代数方程并进行了详细的数值计算．给出了分离区、滑移区和粘着区的分布以及界面应力分布和能量分配;讨论了缝隙宽度、摩擦因数、入射角等因素对波动传输的影响．结果表明:由于界面发生局部接触和滑移使得反射波和透射波中含有高频谐波．缝隙宽度与各阶谐波反射、透射系数的关系可为材料及结构的无损检测提供理论依据．     

各向异性双晶和三晶体晶界附近应力场分析

采用率相关晶体滑移有限元程序对不同取向晶粒构成的双晶体和三晶体在晶界和三晶交点附近的应力集中特性进行了计算分析．双晶体的数值结果表明,不同取向晶粒的晶界附近应力场具有较大的应力梯度,存在应力集中现象;三晶体由于晶界之间的相互作用使得三晶交点可能造成应力集中地,也可能不造成应力集中,晶界附近的应力结构与双晶体晶界附近的应力结构亦不相同,这主要取决于三个晶粒的晶体取向．对双晶体和三晶体的分析说明,不同取向的晶粒具有不同的变形规律．因此研究金属材料的损伤、断裂问题至少需要采用晶体滑移理论从细观的角度分析不同晶粒之间的相互作用．     

基于参数变分原理的非均质材料弹塑性有限元分析的Voronoi单元法

在非均质材料的有限元数值模拟中,采用了Voronoi单元(VCFEM)以克服经典位移元的局限性．基于参数变分原理和二次规划法进行了Voronoi单元的二维弹塑性分析A·D2推导了有限元列式并形成最终的二次规划求解模型．研究了非均质材料微观夹杂对整体力学性能的影响．数值算例证明了该方法的正确和可行性．     

具有立方对称性及两个弛豫时间的微极热弹性介质中调和时间源引起的变形

研究了具有立方对称性及两个弛豫时间的微极热弹性介质在调和时间源中的响应．采用了Fourier变换以及数值逆变换技术．在物理域中,得到了位移、应力、微转动和温度分布的数值结果．将微极立方晶体法向位移、法向力应力、切向耦合应力和温度分布的计算结果,与微极各向同性固体的结果进行比较．绘制了指定材料的数值结果图形．还推断了某些特殊情况的结果．     

辐照下晶体缺陷浓度的自振频域

采用线性化处理、拓扑映射及数值计算相结合的方法，求解了离子辐照下各向同性晶体薄片中缺陷浓度和温度满足的非线性微分方程组，证明了当可控参量，即缺陷产生速度和恒温箱温度处于某些范围时.会出现缺陷浓度和温度的周期性振动这种时间耗散结构.研究了自振频率与辐射条件和晶体性质的依赖关系,并以硅晶体薄片为例．求出了自振频域及特定的几个自振频率和自振振幅．     

Schr(o)dinger方程的时空有限元方法与守恒性

对非线性Schroedinger常微分方程，利用常微分方程连续有限元法证明了能量守恒；对非线性Schroedinger偏微分方程利用时空都连续的全离散有限元方法证明了能量积分守恒和利用空间连续、时间问断的有限元法得到电荷近似守恒，误差为高阶量．并在数值计算上探讨了守恒性和近似程度。结果与理论相吻合．     

双材料接合半无限体三维矩形界面裂纹应力强度因子分析

基于体积力法,研究了双材料接合半无限体三维矩形界面裂纹的应力强度因子问题．在数值计算中,未知的体积力密度采用基本密度函数和多项式乘积的形式来近似,其中基本密度函数是根据界面裂纹应力的振荡奇异性来选取的．计算结果表明,基于本算法得到的数值结果其收敛精度和计算误差都是令人满意的．算例中,给出了应力强度因子随矩形形状及双材料参数的变化规律．     

团簇取样法计算六方晶系GaN晶体中N K-edge电子能量损失谱近阈精细结构

利用多重散射自洽场方法,通过团簇取样计算了晶体的电子能量损失谱精细结构. GaN晶体中N K-edge 近阈结构的计算结果与实验谱线符合得很好.由于理论结果可以对不同能量损失区间的透射电子给出清楚标识,讨论了有关能量过滤像的实验.     

玻壳成型过程诱导残余应力的数值预测

建立了玻壳压制成型固化过程中残余应力预测的数值模拟模型,采用平行平板间玻璃熔体的固化问题来描述成型过程中残余应力形成的机理,并假定材料为热流变简单粘弹性材料．基于板壳理论,将产品视为平板单元的组合,并采用有限元法来求解,这种方法可以象全三维计算一样一层层地计算残余应力,非常适合复杂形状的薄压制成型产品．最后通过实验比较验证了所提出的模型和方法．     

基于人工鱼群算法求任意函数的数值积分

将不等距离分割方法与人工鱼群算法相结合,提出一种基于人工鱼群算法求任意函数数值积分的方法,该方法除能计算通常意义下任意函数的定积分外,还能计算奇异函数积分、振荡函数积分以及原函数不易求得的被积函数的积分.最后给出几个数值积分算例,并与传统数值积分方法作了比较,仿真结果分析表明,该算法十分有效,能够快速有效地获得任意函数的数值积分值.     

A reduced MFE formulation based on POD for the non-stationary conduction-convection problems

In this article, a reduced mixed finite element (MFE) formulation based on proper orthogonal decomposition (POD) for the non-stationary conduction-convection problems is presented. Also the error estimates between the reduced MFE solutions based on POD and usual MFE solutions are derived. It is shown by numerical examples that the results of numerical computation are consistent with theoretical conclusions. Moreover, it is shown that the reduced MFE formulation based on POD is feasible and efficient in finding numerical solutions for the non-stationary conduction-convection problems.     

Refined Numerical Schemes for a Stressed-Strained State of Structural Joints of Layered Elements

A numerical approach based on block-variational modeling of a stressed state of structural joints of layered elements is developed. A refined theory based on a kinematic hypothesis for every layer and joints and numerical results are presented.     

GPU-acceleration of waveform relaxation methods for large differential systems

It is the purpose of this paper to provide an acceleration of waveform relaxation (WR) methods for the numerical solution of large systems of ordinary differential equations. The introduced technique is based on the employ of graphics processing units (GPUs) in order to speed-up the numerical integration process. A CUDA solver based on WR-Picard, WR-Jacobi and red-black WR-Gauss-Seidel iterations is presented and some numerical experiments realized on a multi-GPU machine are provided.     

The set of numerical semigroups of a given genus

In this paper we present a new approach to construct the set of numerical semigroups with a fixed genus. Our methodology is based on the construction of the set of numerical semigroups with fixed Frobenius number and genus. An equivalence relation is given over this set and a tree structure is defined for each equivalence class. We also provide a more efficient algorithm based on the translation of a numerical semigroup to its so-called Kunz-coordinates vector.     

Numerical solution of the three‐dimensional parabolic equation with an integral condition

Developement of numerical methods for obtaining approximate solutions to the three dimensional diffusion equation with an integral condition will be carried out. The numerical techniques discussed are based on the fully explicit (1,7) finite difference technique and the fully implicit (7,1) finite difference method and the (7,7) Crank‐Nicolson type finite difference formula. The new developed methods are tested on a problem. Truncation error analysis and numerical examples are used to illustrate the accuracy of the new algorithms. The results of numerical testing show that the numerical methods based on the finite difference techniques discussed in the present article produce good results. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 193–202, 2002; DOI 10.1002/num.1040     

关于实四元数矩阵的数值半径

本文在[1]的基础上研究了实四元数矩阵的数值半径。得到了关于数值半径幂的不等式。C-数值半径的不等式也给出了。因此我们推广了曹重光教授的结果。     

Mathematical model to analyze the flow and heat transfer problem in U-shaped geothermal exchangers

In this study, we propose a mathematical model for U-shaped geothermal heat exchangers based on the unsteady Navier–Stokes problem. In the numerical solution of this problem, we divide the exchanger into two computational domains: rectilinear pipes where the temperature field is computed analytically, and a U-curved pipe where solutions for both the flow and heat exchange are calculated using a numerical procedure based on the Galerkin finite elements method. The results of some numerical simulations are provided and used to study the performance of geothermal exchangers by assessing the effective energy produced. We also present a validation analysis based on experimental measurements obtained from a real geothermal exchanger.     

混合广义Jacobi和Chebyshev谱配置法求解时间分数阶对流扩散方程

研究时间Caputo分数阶对流扩散方程的高效高阶数值方法.对于给定的时间分数阶偏微分方程,在时间和空间方向分别采用基于移位广义Jacobi函数为基底和移位Chebyshev多项式运算矩阵的谱配置法进行数值求解.这样得到的数值解可以很好地逼近一类在时间方向非光滑的方程解.最后利用一些数值例子来说明该数值方法的有效性和准确性.     

交通流模型基于特征投影分解技术的外推降维有限差分格式

利用特征正交分解(proper orthogonal decomposition,简记为POD)技术研究交通流的Aw-Rascle-Zhang(ARZ)模型. 建立一种基于 POD方法维数较低的外推降维有限差分格式, 并用数值例子检验数值计算结果与理论结果相吻合, 进一步表明基于POD方法的外推降维有限差分格式对于求解交通流方程数值解是可行和有效的.