解非定常不可压缩N-S方程的迭代压力Poisson方程法

１．引 言 数值求解不可压缩流体流动问题可以采用原始变量的方程作为控制方程,也可以用涡量一流函数方程作为控制方程．直接求解原始变量的不可压缩 Ｎａｖｉｅｒ—Ｓｔｏｋｅｓ方程存在一个主要困难：速度向量在每一时刻都必须满足零散度约束条件,即不可压缩性连续方程．用涡量一流函数方程求解时,连续方程自动满足,所以不存在约束条件的问题,但涡量的边界条件比较难处理,且不易应用于三维问题和带有自由表面或其它流体交界面的问题． 解决上述速度向量必须满足零散度约束条件的困难的方法有：人工压缩法［３,１７］;压力Ｐｏｉｓ…     

Navier—Stokes方程组的一个一致有效渐近解

本文利用多重尺度法研究了大雷诺数情况下的平板绕流问题，得到了Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程的一个一致有效渐近解。     

非定常Navier－Stokes方程加罚方法

非定常Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程加罚方法黄艾香，李开泰（西安交通大学应用数学研究中心，西安７１００４９）一、引言非定常Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ初边值问题，有非线性和不可压缩性的困难，加罚方法则是克服不可压缩困难的一种方法，人们常用来代替不可压缩...     

两同心旋转球间流动的弱解的存在唯一性

研究了两个同心旋转球间的轴对称不可压缩的粘性流动。该流动广泛应用于大气物理和地球物理等学科中,为了得到流动的流函数－速度形式的Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程的弱解的存在性和唯一性,首先发现了该方程中非线性项之间关系,并引入一个有限维的辅助问题,通过紧性而得到了结论。     

外部流动的Oseen耦合方法,I:Oseen耦合逼近

这篇文章考虑了具有非齐次边界条件的二维非定常外部Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程．通过将内部区域的Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程和外部区域的Ｏｓｅｅｎ方程相耦合,得到了Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ问题的逼近问题： Ｏｓｅｅｎ耦合问题,此外,我们证明了 Ｏｓｅｅｎ耦合方程弱解的存在性,唯一性和收敛精度．     

Navier－Stokes方程稳定性研究（Ⅰ）

本文给出Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程某种边值问题局部解不唯一性的一个例证。     

Navier—Stokes方程稳定性研究

本给出Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程某种边值问题局部解不唯一性的一个例证。     

偶数维的线性化Navier—Stokes方程解之逐点估计

道德对偶数维线性化Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程的格林函数作出估计，再用格林函数得出了其解的逐点估计。     

粘流－无粘干扰流动理论变分问题迭代序列的收敛性和算子方程性质

本文证明了粘流－无粘干扰流动理论［１，２］基本控制方程─—简化的Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程变分问题几种迭代序列的收敛性，并探讨了其算子方程的性质。本文的结论对于简化Ｎ－Ｓ方程的数值计算具有指导意义。     

二维全空间上线性阻尼Navier-Stokes方程的全局吸引子及其维数估计

本文研究二维全空间上线性阻尼Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程的大时间性态央餐力项ｆ（ｘ）∈（Ｌ＾２（Ｒ＾２）＾２而不需要对ｆ（ｘ）作任何加权限制的条件下,证明了线性阻尼Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程的全局吸引子的存在性,并给出了其Ｈａｕｓｄｏｒｆｆ及Ｆｒａｃｔａｌ维数估计。     

Long-step primal-dual target-following algorithms for linear programming

In this paper we propose a long-step target-following methodology for linear programming. This is a general framework, that enables us to analyze various long-step primal-dual algorithms in the literature in a short and uniform way. Among these are long-step central and weighted path-following methods and algorithms to compute a central point or a weighted center. Moreover, we use it to analyze a method with the property that starting from an initial noncentral point, generates iterates that simultaneously get closer to optimality and closer to centrality.This work is completed with the support of a research grant from SHELL.The first author is supported by the Dutch Organization for Scientific Research (NWO), grant 611-304-028.The fourth author is supported by the Swiss National Foundation for Scientific Research, grant 12-34002.92.     

Trefftz,collocation, and other boundary methods—A comparison

In this article we survey the Trefftz method (TM), the collocation method (CM), and the collocation Trefftz method (CTM). We also review the coupling techniques for the interzonal conditions, which include the indirect Trefftz method, the original Trefftz method, the penalty plus hybrid Trefftz method, and the direct Trefftz method. Other boundary methods are also briefly described. Key issues in these algorithms, including the error analysis, are addressed. New numerical results are reported. Comparisons among TMs and other numerical methods are made. It is concluded that the CTM is the simplest algorithm and provides the most accurate solution with the best numerical stability. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

Volume preserving RK methods for linear systems

1. IntroductionIn recent yearss there has been a great interest in constructing numerical integrationschemes for ODEs in such a way that some qualitative geometrical properties of the solutionof the ODEs are exactly preserved. R.th[ll and Feng Kang[2'31 has proposed symplectic algorithms for Hamiltollian systems, and since then st ruct ure s- preserving me t ho ds fordynamical systems have been systematically developed[4--7]. The symplectic algorithms forHamiltonian systems, the volume-pre…     

求解离散不适定问题的正则化GMERR方法

迭代极小残差方法是求解大型线性方程组的常用方法, 通常用残差范数控制迭代过程.但对于不适定问题, 即使残差范数下降, 误差范数未必下降. 对大型离散不适定问题,组合广义最小误差(GMERR)方法和截断奇异值分解(TSVD)正则化方法, 并利用广义交叉校验准则(GCV)确定正则化参数,提出了求解大型不适定问题的正则化GMERR方法.数值结果表明, 正则化GMERR方法优于正则化GMRES方法.     

A note on the biasing of Newton's direction

This note deals with the geometric interpretation of the Levenberg-Marquardt search direction when the augmented Hessian is not positive definite.     

投入产出技术在计划平衡中的理论与应用

在用投入产出技术作计划平衡时，目前一般采用最终产品法、总产品法及国民收入法等．本文从理论上研究了这些方法的可行性问题，并在此基础上提出一个较理想的综合法．最后附有实例并说明综合法的现实意义．     

Diagonalized multiplier methods and quasi-Newton methods for constrained optimization

Two approaches to quasi-Newton methods for constrained optimization problems inR ⁿ are presented. These approaches are based on a class of Lagrange multiplier approximation formulas used by the author in his previous work on Newton's method for constrained problems. The first approach is set in the framework of a diagonalized multiplier method. From this point of view, a new update rule for the Lagrange multipliers which depends on the particular quasi-Newton method employed is given. This update rule, in contrast to most other update rules, does not require exact minimization of the intermediate unconstrained problem. In fact, the optimal convergence rate is attained in the extreme case when only one step of a quasi-Newton method is taken on this intermediate problem. The second approach transforms the constrained optimization problem into an unconstrained problem of the same dimension.The author would like to thank J. Moré and M. J. D. Powell for comments related to the material in Section 13. He also thanks J. Nocedal for the computer results in Tables 1–3 and M. Wright for the results in Table 4, which were obtained via one of her general programs. Discussions with M. R. Hestenes and A. Miele regarding their contributions to this area were very helpful. Many individuals, including J. E. Dennis, made useful general comments at various stages of this paper. Finally, the author is particularly thankful to R. Byrd, M. Heath, and R. McCord for reading the paper in detail and suggesting many improvements.This work was supported by the Energy Research and Development Administration, Contract No. E-(40-1)-5046, and was performed in part while the author was visiting the Department of Operations Research, Stanford University, Stanford, California.     

s个几乎相等的素数的k次方和(Ⅰ)

假定pθ‖k,当p=2,2|k时，γ=θ 2；其它情况时，γ=θ 1。而R＝П(p-1)|kp^γ。本文在GRH（广义Riemann假设下），证明了当s=2^k 1,1≤k≤11时，任何足够大的整N≡s(modR)都可以表示为s个几乎相等的素数的k次方程。     

A comparison of some ODE solvers which require Jacobian evaluations

A variety of third-order ODE solvers which have a minimum configuration (i.e. minimum work per step) have been numerically tested and the results compared. They include implicit and explicit processes, and share the property that a Jacobian matrix must be evaluated at least once during the integration. Some of these processes have not been previously described in the literature.     

Stabilization of algebraic multilevel iteration methods; additive methods

There exist two main versions of preconditioners of algebraic multilevel type, the additive and the multiplicative methods. They correspond to preconditioners in block diagonal and block matrix factorized form, respectively. Both can be defined and analysed as recursive two-by-two block methods. Although the analytical framework for such methods is simple, for many finite element approximations it still permits the derivation of the strongest results, such as optimal, or nearly optimal, rate of convergence and optimal, or nearly optimal order of computational complexity, when proper recursive global orderings of node points have been used or when they are applied for hierarchical basis function finite element methods for elliptic self-adjoint equations and stabilized in a certain way. This holds for general elliptic problems of second order, independent of the regularity of the problem, including independence of discontinuities of coefficients between elements and of anisotropy. Important ingredients in the methods are a proper balance of the size of the coarse mesh to the finest mesh and a proper solver on the coarse mesh. This paper presents in a survey form the basic results of such methods and considers in particular additive methods. This method has excellent parallelization properties. This revised version was published online in June 2006 with corrections to the Cover Date.