A grid‐free upwind relaxation scheme for inviscid compressible flows

A new grid‐free upwind relaxation scheme for simulating inviscid compressible flows is presented in this paper. The non‐linear conservation equations are converted to linear convection equations with non‐linear source terms by using a relaxation system and its interpretation as a discrete Boltzmann equation. A splitting method is used to separate the convection and relaxation parts. Least squares upwinding is used for discretizing the convection equations, thus developing a grid‐free scheme which can operate on any arbitrary distribution of points. The scheme is grid free in the sense that it works on any arbitrary distribution of points and it does not require any topological information like elements, faces, edges, etc. This method is tested on some standard test cases. To explore the power of the grid‐free scheme, solution‐based adaptation of points is done and the results are presented, which demonstrate the efficiency of the new grid‐free scheme. Copyright © 2005 John Wiley & Sons, Ltd.     

On the spectra of finite-dimensional quadratic Bose operators

A complete study of the spectrum of a finite-dimensional Bose operator is carried out in the paper. The cases in which the spectrum is discrete or continuous are studied. Translated fromMatematicheskie Zametki, Vol. 61, No. 6, pp. 835–854, June, 1997. Translated by A. M. Chebotarev     

Artificial time integration

Many recent algorithmic approaches involve the construction of a differential equation model for computational purposes, typically by introducing an artificial time variable. The actual computational model involves a discretization of the now time-dependent differential system, usually employing forward Euler. The resulting dynamics of such an algorithm is then a discrete dynamics, and it is expected to be “close enough” to the dynamics of the continuous system (which is typically easier to analyze) provided that small – hence many – time steps, or iterations, are taken. Indeed, recent papers in inverse problems and image processing routinely report results requiring thousands of iterations to converge. This makes one wonder if and how the computational modeling process can be improved to better reflect the actual properties sought. In this article we elaborate on several problem instances that illustrate the above observations. Algorithms may often lend themselves to a dual interpretation, in terms of a simply discretized differential equation with artificial time and in terms of a simple optimization algorithm; such a dual interpretation can be advantageous. We show how a broader computational modeling approach may possibly lead to algorithms with improved efficiency. AMS subject classification (2000)  65L05, 65M32, 65N21, 65N22, 65D18     

On Characterizations of Proper Efficiency for Nonconvex Multiobjective Optimization

In this paper, nonconvex multiobjective optimization problems are studied. New characterizations of a properly efficient solution in the sense of Geoffrion's are established in terms of the stability of one scalar optimization problem and the existence of an exact penalty function of a scalar constrained program, respectively. One of the characterizations is applied to derive necessary conditions for a properly efficient control-parameter pair of a nonconvex multiobjective discrete optimal control problem with linear constraints.     

Near-Optimal Controls of Discrete-Time Dynamic Systems Driven by Singularly-Perturbed Markov Chains

This work is devoted to near-optimal controls of large-scale discrete-time nonlinear dynamic systems driven by Markov chains; the underlying problem is to minimize an expected cost function. Our main goal is to reduce the complexity of the underlying systems. To achieve this goal, discrete-time control models under singularly-perturbed Markov chains are introduced. Using a relaxed control representation, our effort is devoted to finding near-optimal controls. Lumping the states in each irreducible class into a single state gives rise to a limit system. Applying near-optimal controls of the limit system to the original system, near-optimal controls of the original system are derived.     

关于“信息熵”分析及其应用的研究

本文用Ｓｈａｎｎｏｎ熵函数的观点及最大离散熵原理，探讨了对随机试验项目的优选问题：即压缩某种“不确定性”试验项目的实施与探索．并通过应用实例的计算，获得了满意的聚类效果．这种方法对于信息资料的数据处理及压缩“不确定性“验项目具有普遍意义．     

Sparse-grid finite-volume multigrid for 3D-problems

We introduce a multigrid algorithm for the solution of a second order elliptic equation in three dimensions. For the approximation of the solution we use a partially ordered hierarchy of finite-volume discretisations. We show that there is a relation with semicoarsening and approximation by more-dimensional Haar wavelets. By taking a proper subset of all possible meshes in the hierarchy, a sparse grid finite-volume discretisation can be constructed.The multigrid algorithm consists of a simple damped point-Jacobi relaxation as the smoothing procedure, while the coarse grid correction is made by interpolation from several coarser grid levels.The combination of sparse grids and multigrid with semi-coarsening leads to a relatively small number of degrees of freedom,N, to obtain an accurate approximation, together with anO(N) method for the solution. The algorithm is symmetric with respect to the three coordinate directions and it is fit for combination with adaptive techniques.To analyse the convergence of the multigrid algorithm we develop the necessary Fourier analysis tools. All techniques, designed for 3D-problems, can also be applied for the 2D case, and — for simplicity — we apply the tools to study the convergence behaviour for the anisotropic Poisson equation for this 2D case.     

既不离散也不连续的随机变量

讨论了既不离散也不连续的随机变量 ,并纠正了有关文献中关于连续型随机变量定义中的错误 .     

关于有限Abel群直接因子的平均数

对于有限Ａｂｅｌ群Ｇ，ｔ（Ｇ）定义为其直接因子的个数，在［５］中，Ｅ．Ｋｒａｔｚｅｌ对于和式得到一渐近公式，对应余项为△＿１（ｘ）．本文利用Ｅ．Ｆｏｕｖｒｙ和Ｈ　．Ｉｗａｎｉｅｃ的方法，得到了关于△＿１（ｘ）的一个新的估计，改进了Ｈ．Ｍｅｎｚｅｒ等人的结果．     

A simple four-node quadrilateral finite element for plates

A simple and accurate four-node quadrilateral finite element based on the Mindlin plate theory and Kirchhoff constraints is presented for general thin plate bending applications. The derivation of the element stiffness properties is straightforward, starting with a specified eight-node interpolation; usual discrete Kirchhoff (DK) constraints are employed to constrain out the four midside nodes of the element. The present resulting DK element passes patch tests with elements of arbitrary and even highly distorted mesh types. Numerical studies of the element convergence behaviours are undertaken for various plate bending problems so far investigated. It is indicated from comparative examples that fairly good convergence characteristics have been achieved.