混合边界条件下的三维定常 旋转Navier-Stokes方程的原始变量有限元计算

本文利用原始变量有限元法求解混合边界条件下的三维定常旋转Navier-Stokes方程,证明了离散问题解的存在唯一性,得到了有限元解的最优误差估计.给出了求解原始变量有限元逼近解的简单迭代算法,并证明了算法的收敛性.针对三维情况下计算资源的限制,采用压缩的行存储格式存储刚度矩阵的非零元素,并利用不完全的LU分解作预处理的GMRES方法求解线性方程组.最后分析了简单迭代和牛顿迭代的优劣对比,数值算例表明在同样精度下简单迭代更节约计算时间.     

Erratum to: Characterization of the Unit Ball in C<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript> Among Complex Manifolds of Dimension <Emphasis Type="Italic">n</Emphasis>

We correct the formulation of the main result in our earlier paper.      

Independent continuous mapping for topological optimization of frame structures

Based on the Independent Continuous Mapping method (ICM), a topological optimization model with continuous topological variables is built by introducing three filter functions for element weight, element allowable stress and element stiffness, which transform the 0-1 type discrete topological variables into continuous topological variables between 0 and 1. Two methods for the filter functions are adopted to avoid the structural singularity and recover falsely deleted elements: the weak material element method and the tiny section element method. Three criteria (no structural singularity, no violated constraints and no change of structural weight) are introduced to judge iteration convergence. These criteria allow finding an appropriate threshold by adjusting a discount factor in the iteration procedure. To improve the efficiency, the original optimization model is transformed into a dual problem according to the dual theory and solved in its dual space. By using MSC/Nastran as the structural solver and MSC/Patran as the developing platform, a topological optimization software of frame structures is accomplished. Numerical examples show that the ICM method is very efficient for the topological optimization of frame structures.The project supported by the National Natural Science Foundation of China (10472003) and Beijing Natural Science Foundation (3042002) The English text was polished by Yunming Chen.     

准静态离散元方法和线性粘弹性问题的模拟

离散元方法是近年发展起来的一种新数值方法,但原则上只能用于动态问题。从静力平衡条件出发建立了离散元系统的准静态演化方程并证明了系数矩阵具有对称正定、稀疏、带状分布等特点,适用于“有效列”方法求解,该解法比高斯消去法节省更多的内存和机时。通过引入广义Maxwell体的元间作用模型建立起线性粘弹性材料准静态响应的离散元模拟方法。该方法独立于传统动态离散元方法,是传统动态离散元方法的拓展,可望在更多领域获得应用。     

Controlling of symmetric and asymmetric mode coupling in long-period fiber gratings singe-side induced by long-pulse CO2 laser

We report a simple fabricating approach to control the mode couplings in long-period fiber gratings (LPFGs) through side exposing fiber to long-pulse-10.6-μm laser from a cheap, internally modulated CO₂ tube. By tuning focused-spot size on fibers, not only circularly symmetric mode coupling but also asymmetric mode couplings can be effectively achieved. Simulation of mode profiles in grating cross-section with Finite Element Method (FEM), and LPFG-cladding etching experiment with hydrofluoric acid (HF), support our explanation that asymmetric mode coupling in LPFGs depends on local refractive-index (RI) change within an azimuthally thin cladding layer, resulted from large-spot method induced deep melt flow on fiber surface during CO₂ laser irradiation.     

激光剥蚀-电感耦合等离子体质谱测定植物样品中的元素

采用193 nm准分子激光剥蚀-电感耦合等离子体质谱(LA-ICP-MS)对标准植物粉末样品(GBW07602-GBW07603灌木枝叶、GBW07604杨树叶、GBW07605茶叶、GBW08514烟草)中13种元素(Li,B,Na,Mg,Al,K,Ca,Cr,Mn,Fe,Ni,Cu,Ba)进行定量测试.向植物粉末样...     

Dual Reciprocity Boundary Element Method for Magnetohydrodynamic Flow Using Radial Basis Functions

A dual reciprocity boundary element method is given to obtain the solution in terms of velocity and induced magnetic field for the study of MHD (magnetohydrodynamic) flow through a rectangular duct having insulating walls. The equations are transformed to two types of nonlinear Poisson equations and the right-hand sides in these equations are approximated using combinations of two classes of radial basis functions (the value of the function and its normal derivatives are utilized for approximation). Computations are carried out for several values of the Hartman number (0 h M h 10) by using constant boundary elements. Comparisons are made for two types of formulations and for traditional and osculatory type approximations of the right-hand side functions. It is found that osculatory interpolation gives better results than traditional interpolation and the type of the Poisson equation, which contains derivative of the unknown function, is better than the other type, which contains unknown function only. The results for velocity and induced magnetic field are illustrated by some selected graphs.     

A stabilized formulation for the advection–diffusion equation using the Generalized Finite Element Method

This paper presents a stable formulation for the advection–diffusion equation based on the Generalized (or eXtended) Finite Element Method, GFEM (or X‐FEM). Using enrichment functions that represent the exponential character of the exact solution, smooth numerical solutions are obtained for problems with steep gradients and high Péclet numbers in one‐ and two‐dimensions. In contrast with traditional stabilized methods that require the construction of stability parameters and stabilization terms, the present work avoids numerical instabilities by improving the classical Galerkin solution with enrichment functions (that need not be polynomials) using GFEM, which is an instance of the partition of unity framework. This work also presents a strategy for constructing enrichment functions for problems involving complex geometries by employing a global–local‐type approach. Representative numerical results are presented to illustrate the performance of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

模糊分析计算中的结构元方法

提出模糊结构元的概念，研究模糊结构元的性质，给出模糊数和模糊值函数的结构元表现定理。利用模糊数和模糊值函数的结构元表现形式，使得过去必须依赖扩张原理和表现定理来刻画的模糊数运算、模糊值函数的微积分运算等变得更加简单与直观。