平面区域四边形网格自动生成技术

本文分析和综述了四边形网格自动生成的各种算法,给出了三角形网格向四边形网格转换的局部算法,以及有FCT思想直接生成四边形和三角形网格算法。详细分析了此法之下生成网格的几何拓朴性质,最后给出实例验证了算法的有效性。     

基于重叠划分的自由网格四边形单元计算方法

提出了一种基于重叠划分的自由网格四边形单元计算方法。这一方法将四边形单元引入到自由网格计算方法中，不仅提高了计算的精度，同时还保留了自由网格计算方法的特点。方法首先对分析域内自动生成的每一个节点建立一套临时三角形单元，利用这些临时三角形单元组合生成四边形单元，以节点为单位进行计算。由于各矩阵的计算与组集均以节点为中心进行处理，因而特别适合于并行计算环境。在详细介绍自由网格四边形单元计算方法的基础上，利用数值算例证实了这一方法改善计算精度方面的有效性。     

Integrating design problems in mathematics curriculum: an architecture college case study

This paper reports an attempt to improve results in the mathematics course in one of the architecture colleges in Israel through practise in applications. The effect of integrating structure design problems in the calculus curriculum on students' achievements and attitudes was examined. The applied topics in the curriculum were connected to calculus topics and studied through problembased learning activities. The integrated curriculum was implemented and the learning results in experimental and control groups were assessed by means of achievement tests, attitude questionnaires and student interviews. The learning achievements in the experimental group proved to be significantly higher than in the control group. The positive impact of learning applications on motivation, understanding, creativity and interest in mathematics is indicated.     

A domain decomposition and mixed method for a linear parabolic boundary value problem

In this paper, we discuss the convergence of a domain decompositionmethod for the solution of linear parabolic equations in theirmixed formulations. The subdomain meshes need not be quasi-uniform;they are composed of triangles or quadrilaterals that do notmatch at interfaces. For the ease of computation, this lackof continuity is compensated by a mortar technique based onpiecewise constant (discontinuous) multipliers. It is shownthat the method on triangles, parallelograms or slightly distortedparallelograms is convergent at the expense of a half-orderloss of accuracy compared with mortar methods based on piecewiselinear multipliers.     

A mixed finite element for the stokes problem using quadrilateral elements

The object of this paper is to complete the results obtained in [3] by showing that the new mixed finite element that we have constructed in [3] also works for quadrilateral elements and to compare this method with the standard finite volume method. Estimates of optimal order are derived for both the new mixed finite element and an associated finite volume method.     

逍遥丸的毛细管电泳指纹图谱的建立

采用毛细管区带电泳法建立了逍遥丸(Xiaoyao Pill, XYP)的毛细管电泳指纹图谱(CEFP)。运用正方形优化法,以色谱指纹图谱分离量指数(RF)为优化的目标函数,对建立指纹图谱的实验条件进行了优化,确定了最佳背景电解质(BGE)溶液50 mmol/L硼砂-50 mmol/L磷酸氢二钠-150 mmol/L磷酸二氢钠-50 mmol/L碳酸氢钠(1:1:1:5, v/v/v/v; pH 7.40)、紫外检测波长228 nm、运行电压12 kV、重力进样25 s (高度14 cm)的分离检测条件。采用未涂层石英毛细管(70 cm×75 μm,有效分离长度57 cm)分离,以咖啡酸色谱峰为参照,确定13批逍遥丸样品的21个共有指纹峰。通过聚类分析确定用其中10批样品生成对照CEFP,以此为标准用系统指纹定量法鉴别13批逍遥丸的质量,结果显示: S3号样品的化学成分数量和分布比例不合格,S10和S12号样品含量明显偏高,其余批次质量均合格。所建立的正方形优化法操作简便,适用于中药的毛细管区带电泳BGE的选择;所建立的逍遥丸CEFP具有较好的精密度和重现性,可以为逍遥丸的质量控制提供新的参考。     

均衡二部图中含2k条指定边的k个独立圈及2-因子

得到了对于二部图G=(V_1,V_2;E),当|V_1|=|V_2|=n≥2k+1时的结果:对G中任意2k条独立边e_1,e_1~*,…,e_k,e_k~*,G中一定存在k个独立的4-圈C_1,C_2,…,C_k,使得对任意i∈{1,2,…,k}有{e_i,e_i~*}E(C_i).并在此基础上进一步证明了当|V_1|=|V_2|=n≥3k时若对任意两顶点x∈V_1,y∈V_2,都有d(x)+d(y)≥2n-k+1成立,则G有一个2-因子含有k+1个独立圈C_1,C_2,…,C_(k+1)使得对任意i∈{1,2,…,k}有{e_i,e_i~*}E(C_i)且|C_i|=4.     

On the quadrilateral Q2–P1 element for the Stokes problem

The Q₂ – P₁ approximation is one of the most popular Stokes elements. Two possible choices are given for the definition of the pressure space: one can either use a global pressure approximation (that is on each quadrilateral the finite element space is spanned by 1 and by the global co‐ordinates x and y) or a local approach (consisting in generating the local space by means of the constants and the local curvilinear co‐ordinates on each quadrilateral ξ and η). The former choice is known to provide optimal error estimates on general meshes. This has been shown, as it is standard, by proving a discrete inf–sup condition. In the present paper we check that the latter approach satisfies the inf–sup condition as well. However, recent results on quadrilateral finite elements bring to light a lack in the approximation properties for the space coming out from the local pressure approach. Numerical results actually show that the second choice (local or mapped pressure approximation) is suboptimally convergent. Copyright © 2002 John Wiley & Sons, Ltd.     

Degenerate scale problem in antiplane elasticity or Laplace equation for contour shapes of triangles or quadrilaterals

This paper provides several solutions to the degenerate scale for the shapes of triangles or quadrilaterals in an exterior boundary value problem (BVP) of the antiplane elasticity or the Laplace equation. The Schwarz-Christoffel mapping is used throughout. It is found that a complex potential with a simple form in the mapping plane satisfies the vanishing displacement condition (or w = 0) along the boundary of the unit circle when the dimension R reaches its critical value 1. This means that the degenerate size in the physical plane is also achieved. The degenerate scales can be evaluated from the particular integrals depending on certain parameters in the mapping function. The numerical results of degenerate sizes for the shapes of triangles or quadrilaterals are provided.     

A 17-node quadrilateral spline finite element using the triangular area coordinates

Isopaxametric quadrilateral elements are widely used in the finite element method. However, they have a disadvantage of accuracy loss when elements are distorted. Spline functions have properties of simpleness and conformality. A 17onode quadrilateral element has been developed using the bivaxiate quaxtic spline interpolation basis and the triangular area coordinates, which can exactly model the quartic displacement fields. Some appropriate examples are employed to illustrate that the element possesses high precision and is insensitive to mesh distortions.