A new general-purpose least-squares finite element model for steady incompressible low-viscosity laminar flow using isoparametric C1-continuous Hermite elements

This paper deals with a critical evaluation of various finite element models for low-viscosity laminar incompressible flow in geometrically complex domains. These models use Galerkin weighted residuals UVP, continuous penalty, discrete penalty and least-squares procedures. The model evaluations are based on the use of appropriate tensor product Lagrange and simplex quadratic triangular elements and a newly developed isoparametric Hermite element. All of the described models produce very accurate results for horizontal flows. In vertical flow domains, however, two different cases can be recognized. Downward flows, i.e. when the gravitational force is in the direction of the flow, usually do not present any special problem. In contrast, laminar flow of low-viscosity Newtonian fluids where the gravitational force is acting in the direction opposite to the flow presents a difficult case. We show that only by using the least-squares method in conjunction with C¹-continuous Hermite elements can this type of laminar flow be modelled accurately. The problem of smooth isoparametric mapping of C¹ Hermite elements, which is necessary in dealing with geometrically complicated domains, is tackled by means of an auxiliary optimization procedure. We conclude that the least-squares method in combination with isoparmetric Hermite elements offers a new general-purpose modelling technique which can accurately simulate all types of low-viscosity incompressible laminar flow in complex domains.     

A Circumradius-Inradius Identity and an Identity Relating Volumes for a Simplex

We establish an identity for an n-dimensional simplex relating the circumradius and the inradius, and an identity relating its volume and the pedal volume. As applications, we derive some known inequalities for simplices and generalizations of such inequalities.     

Error control in the simplex-technique

The present paper describes a simple method to find an indicator of the error in solutions found by a procedure using the simplex-technique, and also describes a method for improving these solutions to any desired accuracy provided certain conditions are met.     

An approximate solution of linear multicriteria control problems through the multicriteria simplex method

This paper deals with multicriteria, linear, continuous optimal control problems through the application of the multicriteria simplex method. Since the system is linear, the state variables at a given time can be expressed in terms of definite integrals. Upon using standard numerical integration formulas, the definite integrals are approximately expressed by means of weighted sums of the integrands. Then, after introducing some suitable auxiliary variables, approximate linear multicriteria programming problems are formulated. Illustrative numerical examples are provided to indicate the efficiency of the proposed method.The author is indebted to Professor Y. Sawaragi of Kyoto University for his constant encouragement. The author also wishes to thank T. Suwa for his cooperation in preparing the programming for the digital computer.     

对线性规划单纯形法的注记

为了更有效地应用单纯形算法求解线性规划问题,本文提出了以下几点注记。(1)人工变量列不必参与数值计算,也不占存储空间,从而可大量节省计算量和存储量;(2)使用基变量指标集来判断人工变量是否离基,可避免舍人误差的影响;(3)虚设人工变量的最终非零值对于修改存在矛盾的数学模型将起着关键性作用;(4)可将大M法与两阶段法统一处理,且M可不取具体的数值,也不参与数值计算;(5)实际计算中宜将Dantzig算法与Bland算法结合起来使用,既可对一般问题达到快速收敛的目的,又可避免退化问题可能产生的循环现象,而且在软件设计与实现上要比字典序方法等简单容易;(6)对于大型稀疏矩阵的计算机数据录入,建议采用二元数组的数据结构逐行录入,则可节省三分之一的录入工作量。     

Column generation decomposition with the degenerate constraints in the subproblem

In this paper, we propose a new Dantzig–Wolfe decomposition for degenerate linear programs with the non degenerate constraints in the master problem and the degenerate ones in the subproblem. We propose three algorithms. The first one, where some set of variables of the original problem are added to the master problem, corresponds to the Improved Primal Simplex algorithm (IPS) presented recently by Elhallaoui et al. [7]. In the second one, some extreme points of the subproblem are added as columns in the master problem. The third algorithm is a mixed implementation that adds some original variables and some extreme points of a subproblem to the master problem. Experimental results on some degenerate instances show that the proposed algorithms yield computational times that are reduced by an average factor ranging from 3.32 to 13.16 compared to the primal simplex of CPLEX.     

Kirchhoff atomic charges fitted to multipole moments: implementation for a virtual screening system

The Kirchhoff charge model is a viable method of generating inexpensive and electrostatically reasonable atomic charges for molecular mechanical force fields. The charging method uses a computationally fast algorithm based on the principle of electronegativity relaxation. Parameters of the method, orbital electronegativities and hardnesses, are fitted to reproduce reference, ab initio calculated dipole and quadrupole moments of a representative training set of neutral and charged organic molecules covering most medicinal chemistry relevant bonding situations. Transferability and accuracy of the derived parameters are confirmed on an external test set. Comparisons to other charge models are made. Implementation of the new Kirchhoff charges into a virtual screening engine is elucidated.     

Operation analysis of natural resources and their pan-weighted network models

In this paper, we propose a competition-share 3-category principle, on which we unite the problems of natural resources, energy, population and environment and so on into a mutual scheme, and provide a united model for the comprehensive research on these problems. This makes the idea of operation analysis of natural resources clearer and the relationships between each of their parts more obvious. On the basis of the above discussion, we propose mathematical models for the operation analysis of multi-networks and the solution of the above global comprehensive problems. We discuss, especially, Shengke (growth and restraint) relationships between two networks of natural resources and share-competitors and their analysis models, providing mathematical tools for solving the problems of the resource-population and the resource-economy, etc. Supported by Science Fund of Lanzhou University.     

“单纯形最佳主元法”的结论欠妥

文献［１］中介绍了求解线性规划问题的“单纯形最佳主元法”,得到了几个重要结论。文章给出反例说明［１］中这几个重要结论不能成立。     

一类非凸不可微规划的算法

讨论一类带非凸不可微函数约束的非凸不可微规划的求解,提出一种基于分枝定界技巧的算法,该算法具有全局收敛性．