一类半线性反应对流扩散模型的特征差分方法和分析

1.引 言如下形式的半线性反应对流扩散方程组分别在生命科学、化学和环境科学中,有大量的应用模型[1-3].其中文献[2-6]分别讨论了方程组(1.1)的各种特殊模型的定性性质.文献[6]讨论了一类线性模型的流线扩散有限元分析.作者在文[7]中,分别利用标准有限元方法和交替方向有限元方法,对(1.1)的一些特殊情形作了数值分析.     

二维稳态各向异性介质渗透率的反演问题

1.引 言由多孔介质的渗流理论,二维稳态各向异性介质的渗流问题满足下列偏微分方程 -div(u(x,y)(?)u(x,y))=f(x,y),(x,y)∈Ω(?)R2, (1.1)     

一类非线性椭圆问题的schwarz算法

其中考虑下述泛函最小问题:求u∈W01,α(Ω),使F(u)=     

定常的热传导-对流问题的Galerkin/Petrov最小二乘混合元方法

1.引言 热传导-对流问题是大气动力学中的一个重要的方程,这个方程组也称为强迫耗散的非线性系统方程组,其较Navier-Stokes方程多了一个未知函数温度场,且温度与速度和压力之间存在着复杂的非线性关系.从热动力学可知,任何运动都会产生热量即有温度,而且温度与速度和压力之间必定互相转化,因此对该非线性系统的研究更具有实际意义.[1]先对     

一类基于变量分离的稳定化混合有限元方法

Based on a seperated model for saddle-point problems, we develop a new sta-bilized mixed finite element method. Such a model consists of two subproblems with respect to the primal and the dual variables, respectively. We show that the new method is coercive and that optimal error bounds hold. As an application,the nearly incompressible elastic problem is analyzed with our method.     

3-正则图的分割问题是NP-完全问题

证明了3-正则图的最小平分问题和最小α-分割问题都是NP-完全问题.     

随机交通均衡配流模型及其等价的变分不等式问题

本文讨论了交通网络系统的随机用户均衡原理的数学表述问题.在路段出行成本是流量的单调函数的较弱条件下,对具有固定需求和弹性需求的模式,首次证明了随机均衡配流模型可表示为一个变分不等式问题,同时也说明了该变分不等式问题与相应的互补问题以及一个凸规划问题之间的等价关系.     

TESTING DIFFERENT CONJUGATE GRADIENT METHODS FOR LARGE—SCALE UNCONSTRAINED OPTIMIZATION

In this PaPer we test different conjugate gradient (CG) methods for solving large-scale unconstrained optimization problems.The methods are divided in two groups:the first group includes five basic CG methods and the second five hybrid CG methods.A collection of medium-scale and large-scale test problems are drawn from a standard code of test problems.CUTE.The conjugate gradient methods are ranked according to the numerical results.Some remarks are given.     

THE INVERSE PROBLEM FOR PART SYMMETRIC MATRICES ON A SUBSPACE

In this paper, the following two problems are considered:Problem Ⅰ. Given S∈E Rn×p,X,B 6 Rn×m, find A ∈ SRs,n such that AX = B, where SR8,n = {A∈ Rn×n|xT(A - AT) = 0, for all x ∈ R(S)}.Problem Ⅱ. Given A* ∈ Rn×n, find A ∈ SE such that ||A-A*|| = minA∈sE||A-A*||, where SE is the solution set of Problem Ⅰ.The necessary and sufficient conditions for the solvability of and the general form of the solutions of problem Ⅰ are given. For problem Ⅱ, the expression for the solution, a numerical algorithm and a numerical example are provided.     

COMPOSITE-STEP LIKE FILTER METHODS FOR EQUALITY CONSTRAINT PROBLEMS

In a composite-step approach, a step sk is computed as the sum of two components vk and hk. The normal component vk, which is called the vertical step, aims to improve the linearized feasibility, while the tangential component hk, which is also called horizontal step, concentrates on reducing a model of the merit functions. As a filter method, it reduces both the infeasibility and the objective function. This is the same property of these two methods. In this paper, one concerns the composite-step like filter approach. That is, a step is tangential component hk if the infeasibility is reduced. Or else, sk is a compositestep composed of normal component Vk and tangential component hk.