Fast unsteady flow computations with a Jacobian-free Newton–Krylov algorithm

Despite the advances in computer power and numerical algorithms over the last decades, solutions to unsteady flow problems remain computing time intensive. Especially for large Reynolds number flows, nonlinear multigrid, which is commonly used to solve the nonlinear systems of equations, converges slowly. The stiffness induced by the large aspect ratio cells and turbulence is not tackled well by this solution method.     

Simpson不等式的改进及其应用

通过一阶导数对Simpson不等式进行了改进,并推导出了相应的数值积分公式和最佳误差限,扩大了Simpson积分公式的适用范围,最后给出了具体的数值应用.     

A Note on the Construction of Crouch-Grossman Methods

Numerical integration methods based on rigid frames were introduced by Crouch and Grossman. The order theory of these methods were later analyzed by Owren and Marthinsen. The resulting order conditions are difficult to solve due to nonlinear relations on the weights of the methods. In this paper we propose a variant of the Crouch-Grossman method that uses modified vector fields so that the order conditions of this new method coincide with the classical order conditions for Runge-Kutta methods.     

Polynomial approximation of functions by means of boundary values and applications: A survey

We collect classical and more recent results on polynomial approximation of sufficiently regular real functions defined in bounded closed intervals by means of boundary values only. The problem is considered from the point of view of the existence of explicit formulas, interpolation to boundary data, bounds for the remainder and convergence of the polynomial series. Applications to some problems of numerical analysis are pointed out, such as nonlinear equations, numerical differentiation and integration formulas, special associated differential boundary value problems. Some polynomial expansions for smooth enough functions defined in rectangles or in triangles of as well as in cuboids or in tetrahedrons in and their applications are also discussed.     

A new numerical quadrature formula on the unit circle

In this paper we study a quadrature formula for Bernstein–Szegő measures on the unit circle with a fixed number of nodes and unlimited exactness. Taking into account that the Bernstein–Szegő measures are very suitable for approximating an important class of measures we also present a quadrature formula for this type of measures such that the error can be controlled with a well-bounded formula. This work was supported by Ministerio de Educación y Ciencia under grants number MTM2005-01320 (E. B. and A. C.) and MTM2006-13000-C03-02 (F. M.).     

我国钢铁行业上市公司竞争力实证研究

钢铁行业是我国的传统行业,在国民经济中具有举足轻重的地位。本文采用主成分分析法,分别从盈利能力、偿债能力、运营能力以及成长能力等方面对我国34家钢铁类上市公司的10项财务指标进行了竞争力综合评价;通过对各个上市公司的分类比较,发现了我国钢铁行业存在的一些问题;最后指出产业整合是提高我国钢铁行业整体竞争力的必要途径。     

Classroom note: Estimation of the cross-product of two mean vectors

The problem of estimating the cross-product of two mean vectors in three-dimensional Euclidian space is considered. Two ‘natural’ estimators are developed, both of which turn out to be biased. A third, unbiased estimator, resulting from a jackknife procedure, is also investigated. It is shown that, under normality, the latter is best among all the unbiased estimators of this quantity.     

On obtaining higher order convergence for smooth periodic functions

We present two algorithms for multivariate numerical integration of smooth periodic functions. The cubature rules on which these algorithms are based use fractional parts of multiples of irrationals in combination with certain weights. Previous work led to algorithms with quadratic and cubic error convergence. We generalize these algorithms so that one can use them to obtain general higher order error convergence. The algorithms are open in the sense that extra steps can easily be taken in order to improve the result. They are also linear in the number of steps and their memory cost is low.     

A finite point method for adaptive three‐dimensional compressible flow calculations

The finite point method (FPM) is a meshless technique, which is based on both, a weighted least‐squares numerical approximation on local clouds of points and a collocation technique which allows obtaining the discrete system of equations. The research work we present is part of a broader investigation into the capabilities of the FPM to deal with 3D applications concerning real compressible fluid flow problems. In the first part of this work, the upwind‐biased scheme employed for solving the flow equations is described. Secondly, with the aim of exploiting the meshless capabilities, an h‐adaptive methodology for 2D and 3D compressible flow calculations is developed. This adaptive technique applies a solution‐based indicator in order to identify local clouds where new points should be inserted in or existing points could be safely removed from the computational domain. The flow solver and the adaptive procedure have been evaluated and the results are encouraging. Several numerical examples are provided in order to illustrate the good performance of the numerical methods presented. Copyright © 2008 John Wiley & Sons, Ltd.     

Gauss legendre quadrature formulas over a tetrahedron

In this article we consider the Gauss Legendre Quadrature method for numerical integration over the standard tetrahedron: {(x, y, z)|0 ≤ x, y, z ≤ 1, x + y + z ≤ 1} in the Cartesian three‐dimensional (x, y, z) space. The mathematical transformation from the (x, y, z) space to (ξ, η, ζ) space is described to map the standard tetrahedron in (x, y, z) space to a standard 2‐cube: {(ξ, η, ζ)| ? 1 ≤ ζ, η, ζ ≤ 1} in the (ξ, η, ζ) space. This overcomes the difficulties associated with the derivation of new weight coefficients and sampling points. The effectiveness of the formulas is demonstrated by applying them to the integration of three nonpolynomial, three polynomial functions and to the evaluation of integrals for element stiffness matrices in linear three‐dimensional elasticity. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006