Approximation for Navier-Stokes equations around a rotating obstacle

This work presents an approximation method for Navier-Stokes equations around a rotating obstacle. The detail of this method is that the exterior domain is truncated into a bounded domain and a new exterior domain by introducing a large ball. The approximation problem is composed of the nonlinear problem in the bounded domain and the linear problem in the new exterior domain. We derive the approximation error between the solutions of Navier-Stokes equations and the approximation problem.     

A decomposition approximation method for multiclass BCMP queueing networks with multiple-server stations

Closed multiclass separable queueing networks can in principle be analyzed using exact computational algorithms. This, however, may not be feasible in the case of large networks. As a result, much work has been devoted to developing approximation techniques, most of which is based on heuristic extensions of the mean value analysis (MVA) algorithm. In this paper, we propose an alternative approximation method to analyze large separable networks. This method is based on an approximation method for non-separable networks recently proposed by Baynat and Dallery. We show how this method can be efficiently used to analyze large separable networks. It is especially of interest when dealing with networks having multiple-server stations. Numerical results show that this method has good accuracy.     

有理曲线的多项式逼近

利用曲线摄动的思想给出了用多项式曲线逼近有理曲线的一种新方法．其基本步骤是对有理曲线的控制顶点进行摄动，使之产生一多项式曲线，并使摄动误差在某种范数意义之下达到最小．同时，通过适当控制摄动曲线的顶点，使逼近多项式曲线与有理曲线在两端点保持一定的连续性．这一结果可以与细分（ｓｕｂｄｉｖｉｓｉｏｎ）技术结合给出有理曲线的整体光滑的分片多项式逼近．实例表明，在某些情况下本文中的方法要优于传统的Ｈｅｒｍｉｔｅ插值方法及Ｔ．Ｗ．Ｓｅｄｅｒｂｅｒｇ和Ｍ．Ｋａｋｉｍｏｔｏ（１９９１）提出的杂交曲线逼近算法．     

由Fourier系数确定的函数类的最佳m-项单边逼近渐近估计

结合最佳m项逼近和单边逼近的思想引进所谓最佳m项单边逼近的概念,给出由Fourier系数确定的光滑函数类通过三角函数系在Lp(1≤P≤∞)的最佳m-项单边逼近渐近估计以及m-项类贪婪单边逼近结果.     

Une méthode particulaire déterministe pour des équations diffusives non linéaires

We study in this Note a deterministic particle method for heat (or Fokker–Planck) equations or for porous media equations. This method is based upon an approximation of these equations by nonlinear transport equations and we prove the convergence of that approximation. Finally, we present some numerical experiments for the heat equation and for an example of porous media equations.     

An approximation method using approximate approximations

The aim of this article is to extend the method of approximate approximations to boundary value problems. This method was introduced by V. Maz'ya in 1991 and has been used until now for the approximation of smooth functions defined on the whole space and for the approximation of volume potentials. In the present article we develop an approximation procedure for the solution of the interior Dirichlet problem for the Laplace equation in two dimensions using approximate approximations. The procedure is based on potential theoretical considerations in connection with a boundary integral equations method and consists of three approximation steps as follows. In the first step, the unknown source density in the potential representation of the solution is replaced by approximate approximations. In the second, the decay behavior of the generating functions is used to gain a suitable approximation for the potential kernel, and in the third, Nyström's method leads to a linear algebraic system for the approximate source density. For every step a convergence analysis is established and corresponding error estimates are given.     

Analysis of the complex moving least squares approximation and the associated element-free Galerkin method

The complex moving least squares approximation is an efficient method to construct approximation functions in meshless methods. This paper begins by analyzing properties, stability and error of the approximation. To overcome the inherent instability, a stabilized approximation is also developed and analyzed. The complex element-free Galerkin method is a meshless method combined with the use of the complex moving least squares approximation. Application of the complex element-free Galerkin method to linear and nonlinear time-dependent problems is then given. Error estimates of the complex element-free Galerkin method are derived theoretically. Numerical examples involving function fitting and solitons are finally provided to show the accuracy and efficiency of the proposed methods.     

A dual interpolation boundary face method with Hermite-type approximation for potential problems

This paper presents the dual interpolation boundary face method combined with a Hermite-type moving-least-squares approximation for solving complex two-dimensional potential problems. Compared to the standard algorithms, this combined method is better suited for structures with small feature sizes such as short edges and small chamfers. The interpolation functions, if constructed in cyclic coordinates, making it difficult to apply this new method to deal with complex structures with small feature sizes in which only one source point is assigned. The Hermite-type approximation formulated in Cartesian coordinates is able to completely overcome this obstacle by searching for source points on adjacent edges. Additionally, an improved and incomplete quadratic polynomial basis is presented to obtain an accurate algorithm for the Hermite-type approximation. We use several numerical examples to demonstrate the high accuracy and efficiency of the proposed method for solving various engineering structures with small feature sizes.     

Saddlepoint Approximations to the Probability of Ruin in Finite Time for the Compound Poisson Risk Process Perturbed by Diffusion

A large deviations type approximation to the probability of ruin within a finite time for the compound Poisson risk process perturbed by diffusion is derived. This approximation is based on the saddlepoint method and generalizes the approximation for the non-perturbed risk process by Barndorff-Nielsen and Schmidli (Scand Actuar J 1995(2):169–186, 1995). An importance sampling approximation to this probability of ruin is also provided. Numerical illustrations assess the accuracy of the saddlepoint approximation using importance sampling as a benchmark. The relative deviations between saddlepoint approximation and importance sampling are very small, even for extremely small probabilities of ruin. The saddlepoint approximation is however substantially faster to compute.     

Approximate solutions and error estimates for a Stokes boundary value problem

The aim of this paper is the numerical treatment of a boundary value problem for the system of Stokes’ equations. For this we extend the method of approximate approximations to boundary value problems. This method was introduced by Maz’ya (DFG-Kolloquium des DFG-Forschungsschwerpunktes Randelementmethoden, 1991) and has been used until now for the approximation of smooth functions defined on the whole space and for the approximation of volume potentials. In the present paper we develop an approximation procedure for the solution of the interior Dirichlet problem for the system of Stokes’ equations in two dimensions. The procedure is based on potential theoretical considerations in connection with a boundary integral equations method and consists of three approximation steps as follows. In a first step the unknown source density in the potential representation of the solution is replaced by approximate approximations. In a second step the decay behavior of the generating functions is used to gain a suitable approximation for the potential kernel, and in a third step Nyström’s method leads to a linear algebraic system for the approximate source density. For every step a convergence analysis is established and corresponding error estimates are given.     

Nonlinear Chebyshev fitting from the solution of ordinary differential equations

The nonlinear Chebyshev approximation of real-valued data is considered where the approximating functions are generated from the solution of parameter dependent initial value problems in ordinary differential equations. A theory for this process applied to the approximation of continuous functions on a continuum is developed by the authors in [17]. This is briefly described and extended to approximation on a discrete set. A much simplified proof of the local Haar condition is given. Some algorithmic details are described along with numerical examples of best approximations computed by the Exchange algorithm and a Gauss-Newton type method.     

Convergence and optimal complexity of adaptive finite element eigenvalue computations

In this paper, an adaptive finite element method for elliptic eigenvalue problems is studied. Both uniform convergence and optimal complexity of the adaptive finite element eigenvalue approximation are proved. The analysis is based on a certain relationship between the finite element eigenvalue approximation and the associated finite element boundary value approximation which is also established in the paper. This work was partially supported by the National Science Foundation of China under grant 10425105 and the National Basic Research Program under grant 2005CB321704.     

Approximation Methods by Regular Functions

This paper is a survey of approximation results and methods by smooth functions in Banach spaces. The topics considered in the paper are the following: approximation by polynomials by C^k-functions using the method of smooth partitions of unity, approximation by the fine topology, analytic approximation and regularization in Banach spaces using the infimal convolution method.     

APPROXIMATION OF SOLUTION OF LINEAR DIFFERENTIAL EQUATION WITH ALMOST PERIOD FUNCTION COEFFICIENTS

Let us consider fOllowing the linear differential equation system:We transfrom this system to vector-matrix form:whereand writeTheorem 1 Suppose that the coefficient matrixs A*(t) and A**(t) aIld tl1e frec terIllvectors W*(t) and W**(t) of the lillear differe1ltial equationsare L-iIltegrablc in tlle interval (a, oo) a11dwllere A1, A2, B1 a11d B2 are constants, E a11d n axe sma1l constants.If Y*(t) aIl相似文献   

自适应稀疏伪谱逼近新方法

自适应稀疏伪谱逼近法是广义混沌多项式类方法的最新进展,相对于其它方法具有计算精度高、速度快的优点.但它仍存在如下缺点：1）终止判据对逼近误差的估计精度偏低;2）只适用于单输出问题.本文提出了适用于多输出问题且具有更高逼近精度的自适应稀疏伪谱逼近新方法.本文首先提出了新型终止判据及基于此新型终止判据的自适应稀疏伪谱逼近新方法,并以命题的形式证明了新型终止判据相比于现有终止判据具有更高的估计精度,从而使基于此的逼近函数精度更接近于预期精度;进而,本文基于指标集的统一策略和新型终止判据,提出了适用于多输出问题的自适应稀疏伪谱逼近新方法,该方法因能充分利用各输出变量的抽样结果,具有比将单输出方法直接推广到多输出问题更高的计算效率.多个算例验证了本文所提出新方法的有效性和正确性.     

A new cubic B-spline method for linear fifth order boundary value problems

In this paper, we mainly study the numerical solution of linear fifth order boundary value problems by using cubic B-splines. Our algorithm develops not only the cubic spline approximation solution but also the approximation derivatives of first order to fourth order of the analytic solution at the same time. This new method has lower computational cost than many other methods and is second order convergent. Numerical examples are given to demonstrate the effectiveness of our method.     

On the nearest parametric approximation of a fuzzy number

Many nearest parametric approximation methods of fuzzy sets are proposed in the literature. It is clear that the specific approximations may lead to the loss of information about fuzziness. To overcome this problem, most of these methods rely on the minimization of the distance between the original fuzzy set and its approximation. But these approximations mostly are not flexible to the decision maker's choice. Hence, in this paper, we offer a parametric fuzzy approximation method based on the decision maker's strategy as an extension of trapezoidal approximation of a fuzzy number. This method comprises the selection of the form of the parametric membership function and its evaluation.     

Discrete extrinsic curvatures and approximation of surfaces by polar polyhedra

Duality principle for approximation of geometrical objects (also known as Eu-doxus exhaustion method) was extended and perfected by Archimedes in his famous tractate “Measurement of circle”. The main idea of the approximation method by Archimedes is to construct a sequence of pairs of inscribed and circumscribed polygons (polyhedra) which approximate curvilinear convex body. This sequence allows to approximate length of curve, as well as area and volume of the bodies and to obtain error estimates for approximation. In this work it is shown that a sequence of pairs of locally polar polyhedra allows to construct piecewise-affine approximation to spherical Gauss map, to construct convergent point-wise approximations to mean and Gauss curvature, as well as to obtain natural discretizations of bending energies. The Suggested approach can be applied to nonconvex surfaces and in the case of multiple dimensions.     

Galerkin method for Wiener-Hopf operators with piecewise continuous symbol

This paper is concerned with the applicability of maximum defect polynomial (Galerkin) spline approximation methods with graded meshes to Wiener-Hopf operators with matrix-valued piecewise continuous generating function defined on R. For this, an algebra of sequences is introduced, which contains the approximating sequences we are interested in. There is a direct relationship between the stability of the approximation method for a given operator and invertibility of the corresponding sequence in this algebra. Exploring this relationship, the methods of essentialization, localization and identification of the local algebras are used in order to derive stability criteria for the approximation sequences.Supported by grant Praxis XXI/BD/4501/94 from FCT.Partly supported by FCT/BMFT grant 423.     

Adaptive Algorithm for Constrained Least-Squares Problems

This paper is concerned with the implementation and testing of an algorithm for solving constrained least-squares problems. The algorithm is an adaptation to the least-squares case of sequential quadratic programming (SQP) trust-region methods for solving general constrained optimization problems. At each iteration, our local quadratic subproblem includes the use of the Gauss–Newton approximation but also encompasses a structured secant approximation along with tests of when to use this approximation. This method has been tested on a selection of standard problems. The results indicate that, for least-squares problems, the approach taken here is a viable alternative to standard general optimization methods such as the Byrd–Omojokun trust-region method and the Powell damped BFGS line search method.