A Compact Fourth-Order Finite Difference Scheme for Unsteady Viscous Incompressible Flows

In this paper, we extend a previous work on a compact scheme for the steady Navier–Stokes equations [Li, Tang, and Fornberg (1995), Int. J. Numer. Methods Fluids, 20, 1137–1151] to the unsteady case. By exploiting the coupling relation between the streamfunction and vorticity equations, the Navier–Stokes equations are discretized in space within a 3×3 stencil such that a fourth order accuracy is achieved. The time derivatives are discretized in such a way as to maintain the compactness of the stencil. We explore several known time-stepping approaches including second-order BDF method, fourth-order BDF method and the Crank–Nicolson method. Numerical solutions are obtained for the driven cavity problem and are compared with solutions available in the literature. For large values of the Reynolds number, it is found that high-order time discretizations outperform the low-order ones.     

供应链集成化模型与优化

本文建立了一个包括供应商、制造商、销售商 在内的集成化模型,这一模型含有线性状态方程和神经网络非线性模型,提出了库存成本、 供应成本、生产水平等在内的供应链目标函数和约束条件．对于供应链集成化模型采用模拟 退火方法进行优化,并以辽化公司为背景进行了初步条件的仿真工作．     

Form finding of shells by structural optimization

Shell structures are known to be extremely parameter sensitive; even small changes of the initial design, e.g., to the shape of the shell, may drastically change the internal stress state. The ideal case for concrete shells is a pure membrane stress state in compression for all loading conditions. Since in many realistic situations the solution for an optimal shape is not obvious, the need for form finding methods is evident. This paper presents computational methods of structural optimization as a general tool for the form finding of shells. The procedure as a synthesis of design modelling, structural analysis and mathematical optimization is discussed with special emphasis on the modelling stage. Several examples show the power of the approach and the similarities to experimental solutions.     

Optimizing multiple dimensional queries simultaneously in multidimensional databases

Some significant progress related to multidimensional data analysis has been achieved in the past few years, including the design of fast algorithms for computing datacubes, selecting some precomputed group-bys to materialize, and designing efficient storage structures for multidimensional data. However, little work has been carried out on multidimensional query optimization issues. Particularly the response time (or evaluation cost) for answering several related dimensional queries simultaneously is crucial to the OLAP applications. Recently, Zhao et al. first exploited this problem by presenting three heuristic algorithms. In this paper we first consider in detail two cases of the problem in which all the queries are either hash-based star joins or index-based star joins only. In the case of the hash-based star join, we devise a polynomial approximation algorithm which delivers a plan whose evaluation cost is $ O(n^{\epsilon }$) times the optimal, where n is the number of queries and is a fixed constant with . We also present an exponential algorithm which delivers a plan with the optimal evaluation cost. In the case of the index-based star join, we present a heuristic algorithm which delivers a plan whose evaluation cost is n times the optimal, and an exponential algorithm which delivers a plan with the optimal evaluation cost. We then consider a general case in which both hash-based star-join and index-based star-join queries are included. For this case, we give a possible improvement on the work of Zhao et al., based on an analysis of their solutions. We also develop another heuristic and an exact algorithm for the problem. We finally conduct a performance study by implementing our algorithms. The experimental results demonstrate that the solutions delivered for the restricted cases are always within two times of the optimal, which confirms our theoretical upper bounds. Actually these experiments produce much better results than our theoretical estimates. To the best of our knowledge, this is the only development of polynomial algorithms for the first two cases which are able to deliver plans with deterministic performance guarantees in terms of the qualities of the plans generated. The previous approaches including that of [ZDNS98] may generate a feasible plan for the problem in these two cases, but they do not provide any performance guarantee, i.e., the plans generated by their algorithms can be arbitrarily far from the optimal one. Received: July 21, 1998 / Accepted: August 26, 1999     

基于有限障碍的全牛顿步内点算法

针对线性规划问题,文中引入了一种与传统障碍函数不同的新的障碍函数,其在可行域边界上的取值是有限的.沿此有限障碍函数所确定的新的搜索方向,给出了短步长全牛顿步内点算法,结果证明该算法具有目前求解线性规划问题最好的复杂性界.     

A Tabu search algorithm for the network pricing problem

In this paper, we propose an efficient Tabu Search procedure for solving the NP-hard network pricing problem. By exploiting the problem's features, the algorithm allows the near-optimal solution of problem instances that are out of reach of exact combinatorial methods.     

Optimal error estimates of the penalty method for the linearized viscoelastic flows

In this article, optimal error estimates of the penalty method for the linearized viscoelastic flows equations arising in the Oldroyd model are derived. Furthermore, error estimates for the backward Euler time discretization scheme in L ² and H ¹-norms are obtained.     

Fourth-order accurate BLAGE iterative method for the solution of two-dimensional elliptic equations in polar co-ordinates

In this article, we report on the block alternating group explicit (BLAGE) iterative method for solving the block symmetric linear system derived from the fourth-order accurate nine-point discretisation of a two-dimensional elliptic equation in cylindrical polar co-ordinates. The error analysis of the BLAGE method is discussed briefly. The performance of this more accurate BLAGE method is compared with the corresponding block successive over relaxation (BSOR) method by considering two test problems, wherein the significance of the role played by two parameters ω₁ and ω₂ of the BLAGE method becomes evident in providing both convergence and accuracy of the computed solution.