Numerical solution of three-dimensional boundary-value problems by generalized approximate inverse matrix techniques

Generalized Approximate Inverse Matrix (GAIM) techniques based on the concept of LU-type sparse factorization procedures are introduced for calculating explicitly approximate inverses of large sparse unsymmetric matrices of regular structure without inverting the factors L and U. Explicit first and second-order iterative methods in conjunction with modified forms of the GAIM techniques are presented for solving numerically three-dimensional initial/boundary-value problems on multiprocessor systems. Applications of the new methods on a 3D boundary-value problem is discussed and numerical results are given.     

Piecewise-linearized and linearized θ-methods for ordinary and partial differential equations

Initial- and boundary-value problems appear frequently in many branches of physics. In this paper, several numerical methods, based on linearization techniques, for solving these problems are reviewed. First, piecewise-linearized methods and linearized θ-methods are considered for the solution of initial-value problems in ordinary differential equations. Second, piecewise-linearized techniques for two-point boundary-value problems in ordinary differential equations are developed and used in conjunction with a shooting method. In order to overcome the lack of convergence associated with shooting, piecewise-linearized methods which provide piecewise analytical solutions and yield nonstandard finite difference schemes are presented. Third, methods of lines in either space or time for the solution of one-dimensional convection-reaction-diffusion problems that transform the original problem into an initial- or boundary-value one are reviewed. Methods of lines in time that result in boundary-value problems at each time step can be solved by means of the techniques described here, whereas methods of lines in space that yield initial-value problems and employ either piecewise-linearized techniques or linearized θ-methods in time are also developed. Finally, for multidimensional problems, approximate factorization methods are first used to transform the multidimensional problem into a sequence of one-dimensional ones which are then solved by means of the linearized and piecewise-linearized methods presented here.     

Evolutionary algorithms for constrained engineering problems

Evolutionary computation techniques have been receiving increasing attention regarding their potential as optimization techniques for complex problems. Recently these techniques were applied in the area of industrial engineering; the most-known applications include scheduling and sequencing in manufacturing systems, computer-aided design, facility layout and location problems, distribution and transportation problems, and many others. Industrial engineering problems usually are quite hard to solve due to a high complexity of the objective functions and a significant number of problem-specific constraints; often an algorithm to solve such problems requires incorporation of some heuristic methods. In this paper we concentrate on constraint handling heuristics for evolutionary computation techniques. This general discussion is followed by three test case studies: truss structure optimization problem, design of a composite laminated plate, and the unit commitment problem. These are typical highly constrained engineering problems and the methods discussed here are directly transferrable to industrial engineering problems.     

Symbolic elimination in dynamic optimization based on block-triangular ordering

We consider dynamic optimization problems for systems described by differential-algebraic equations (DAEs). Such problems are usually solved by discretizing the full DAE. We propose techniques to symbolically eliminate many of the algebraic variables in a preprocessing step before discretization. These techniques are inspired by the causalization and tearing techniques often used when solving DAE initial value problems. Since sparsity is crucial for some dynamic optimization methods, we also propose a novel approach to preserving sparsity during this procedure. The proposed methods have been implemented in the open-source JModelica.org platform. We evaluate the performance of the methods on a suite of optimal control problems solved using direct collocation. We consider both computational time and probability of solving the problem in a timely manner. We demonstrate that the proposed methods often are an order of magnitude faster than the standard way of discretizing the full DAE, and also significantly increase probability of successful convergence.     

基于.NET的管理信息系统与Excel传递和交换数据

微软的Excel是应用非常广泛的电子表格软件。如何在基于.NET技术的管理信息系统中与Excel传递和交换数据是广大程序开发人员要面对的问题。本文结合VB.NET中的实例来讨论解决这个问题的方法和技巧。这些方法和技巧在开发基于.NET技术的管理信息系统中很有实用价值。     

多元统计方法在故障诊断中的应用综述

在对常用故障诊断方法进行简单介绍的基础上,着重对多元统计方法在故障诊断领域的应用进行综述。针对常规方法在解决非线性、时变动态、故障隔离和辨识等问题的缺陷,总结了不同学者解决这些问题的最新进展。最后给出了多元统计方法在工业过程故障诊断领域可能的发展方向。     

A class of explicit preconditioned conjugate gradient methods for solving large finite element systems

A class of Explicit Preconditioned Conjugate Gradient (EPCG) methods for solving large sparse linear systems of algebraic equations resulting from the Finite Element discretization of Elliptic and Parabolic PDE's is introduced. The EPCG methods are based on explicit Approximate Inverse Matrix techniques and are particularly suitable for solving numerically initial/boundary-value problems on multiprocessor systems. The application of the new methods on 2D-linear boundary-value problems is discussed and numerical results are given.     

An adaptive local binarization method for document images based on a novel thresholding method and dynamic windows

Binary image representation is essential format for document analysis. In general, different available binarization techniques are implemented for different types of binarization problems. The majority of binarization techniques are complex and are compounded from filters and existing operations. However, the few simple thresholding methods available cannot be applied to many binarization problems. In this paper, we propose a local binarization method based on a simple, novel thresholding method with dynamic and flexible windows. The proposed method is tested on selected samples called the DIBCO 2009 benchmark dataset using specialized evaluation techniques for binarization processes. To evaluate the performance of our proposed method, we compared it with the Niblack, Sauvola and NICK methods. The results of the experiments show that the proposed method adapts well to all types of binarization challenges, can deal with higher numbers of binarization problems and boosts the overall performance of the binarization.     

GMRES implementations and residual smoothing techniques for solving ill-posed linear systems

There are verities of useful Krylov subspace methods to solve nonsymmetric linear system of equations. GMRES is one of the best Krylov solvers with several different variants to solve large sparse linear systems. Any GMRES implementation has some advantages. As the solution of ill-posed problems are important. In this paper, some GMRES variants are discussed and applied to solve these kinds of problems. Residual smoothing techniques are efficient ways to accelerate the convergence speed of some iterative methods like CG variants. At the end of this paper, some residual smoothing techniques are applied for different GMRES methods to test the influence of these techniques on GMRES implementations.     

Numerical solution of non-linear elliptic boundary-value problems by isomorphic iterative methods

New implicit iterative methods are presented for the efficient numerical solution of non-linear elliptic boundary-value problems. Isomorphic iterative schemes in conjunction with preconditioning techniques are used for solving non-linear elliptic equations in two and three-space dimensions. The application of the derived methods on characteristic 2D and 3D non-linear boundary-value problems is discussed and numerical results are given.     

Conforming Chebyshev spectral methods for Poisson problems in rectangular domains

Four and six-element conforming domain decomposition techniques are developed for Chebyshev spectral collocation methods for Poisson problems in rectangular domains. The applicability of the methods is demonstrated on standard test problems.Parts of this work were performed while the author was at the Mathematics Department, Southern Methodist University, Dallas, Texas 75275.     

The Analytical Hierarchy Process for contaminated land management

Decision analysis (DA) methods and techniques are used to support decision-makers deal with complexities, uncertainties and risks of contaminated land management problems. Over the years, several methods have been used for environmental decision-making. This paper reviews the different methods and techniques used for contaminated land decision-making and decision analysis. We focus on the Analytic Hierarchy Process, which is among the most widely used and fastest growing decision-analytic techniques in several disciplines, including environmental and resource planning and management. However its application to contaminated land management problems as yet has been minimal and under explored. We explore the potential of this technique and explain it with a simple case study.     

Iterative rule induction methods

We examine heuristic techniques for inducing production rules to cover artificially generated boolean expressions with irrelevant noise attributes. The results of different rule induction methods are compared, and it is shown that an iterative tree-based single-best-rule technique performs best on a set of widely-studied applications. We also introduce a new class of iterative Swap-1 rule induction techniques that also solve these problems. While the primary focus is on rule-based solutions, the results for k-nearest neighbor methods and back-propagation neural networks are also reviewed. The results cannot be immediately extrapolated to the more general class of problems with unknown distributions and numerical variables. However, they do offer some comparisons of the effectiveness of competitive rule induction methods that use substantially the same representation.     

Explicit preconditioned domain decomposition schemes for solving nonlinear boundary value problems

A new class of inner-outer iterative procedures in conjunction with Picard-Newton methods based on explicit preconditioning iterative methods for solving nonlinear systems is presented. Explicit preconditioned iterative schemes, based on the explicit computation of a class of domain decomposition generalized approximate inverse matrix techniques are presented for the efficient solution of nonlinear boundary value problems on multiprocessor systems. Applications of the new composite scheme on characteristic nonlinear boundary value problems are discussed and numerical results are given.     

SMT求解器理论组合技术研究

可满足模理论(SMT)求解器是计算机科学中用来判定一阶逻辑公式可满足性的程序,是许多形式化方法的验证引擎.理论求解器实现了SMT基于不同理论背景的求解过程,然而实际问题常以多个理论为背景.因此,本文重点介绍理论组合判定方法,概述SMT求解器的发展现状,并分析了几个主流SMT求解器理论组合判定关键技术.通过对照实验,评估...     

Partitioned Simulation of Fluid-Structure Interaction

In this review article, the focus is on partitioned simulation techniques for strongly coupled fluid-structure interaction problems, especially on techniques which use at least one of the solvers as a black box. First, a number of analyses are reviewed to explain why Gauss–Seidel coupling iterations converge slowly or not at all for fluid-structure interaction problems with strong coupling. This provides the theoretical basis for the fast convergence of quasi-Newton and multi-level techniques. Second, several partitioned techniques that couple two black-box solvers are compared with respect to implementation and performance. Furthermore, performance comparisons between partitioned and monolithic techniques are examined. Subsequently, two similar techniques to couple a black-box solver with an accessible solver are analyzed. In addition, several other techniques for fluid-structure interaction simulations are studied and various methods to take into account deforming fluid domains are discussed.     

Integral least-squares techniques for frequency-domain model reduction

Three different techniques for linear SISO system model reduction are presented. Each method is based on an integral error criterion in the frequency domain which is derived from an equivalent time-domain criterion. Two of the methods are of the linear least-squares class and are therefore easily solved. The third method falls into the broad class of non-linear least-squares problems and demands the use of a powerful optimization technique. The efficiency of each of the methods is compared to previous curve-fitting least-squares techniques and recommendations for their use are made.     

SYSTEM PROBLEMS AND COMPUTER TECHNIQUES: NUMERICAL VS. EXPERT SYSTEM APPROACHES

Programming techniques suitable for systems problems are discussed. It is proposed that APL and APL2 would be particularly suitable for numerical modelling, while certain types of expert systems methods would be appropriate for problems dealing with large scale searches, especially when using heuristics. It is suggested that these expert systems can and should be based on the Ada language. Following a general discussion of pro's and con's, a novel approach based on Ada concurrent features is discussed. These techniques that Ad a provides allow for substitution of parallel processing for backtracking. The recommendations are illustrated with case studies. The actual experiences with using these methods are also discussed.     

复杂工业过程质量相关的故障检测与诊断技术综述

质量相关的故障检测与诊断技术是保证安全生产及获得可靠产品质量的有效手段,是当前国际过程控制领域的研究热点.首先,梳理了质量相关的故障检测技术中典型方法的基本思想和改进过程;其次,概述了质量相关的故障诊断技术中常用的贡献图法及其相关改进方法之间的联系,并通过带钢热连轧过程（Hot strip mill process,HSMP）案例比较了各种典型方法在质量相关的故障检测与诊断性能上的异同;最后,面向复杂工业过程运行数据的主要特性,评析了质量相关的故障检测与诊断方法的研究现状,并指出了该研究领域亟需解决的问题和未来的发展方向.     

Nonsmooth computational mechanics algorithms, quasidifferentiability and related topics

Several extensions of smooth computational mechanics algorithms for the treatment of nonsmooth and possible nonconvex problems are briefly discussed in this paper. A potential or dissipation energy minimization problem approach is used for the structural analysis problem, so as to make the link with mathematical optimization techniques straightforward. Variational inequality problems, hemivariational inequality problems and systems of variational inequalities can be treated by the methods reviewed in this paper. The use of quasidifferentiable and codifferentiable optimization techniques is proposed for the solution of the more general class of nonconvex, possibly nonsmooth problems. Established and new directions in path-following techniques are discussed and are linked with nonsmooth mechanics algorithms.