带1-范数约束的分裂可行问题的投影算法

本文主要研究带1-范数约束的分裂可行问题的求解算法.用一种交替投影算法,求得了问题的解,提出松弛交替投影算法,改进了直接往闭凸集上投影这一不足,并证明了该算法的收敛性.     

Numerical solution of a singular integral equation arising in a cruciform crack problem

A singular integral equation arising in a cruciform crack problem is investigated in the present paper. Based on the convex technique, the piecewise Taylor-series expansion method is extended by introducing a weight parameter. An approximate solution of the singular integral equation is constructed and its convergence and error estimate are made. The variations of the approximate solutions associating with stress intensity factors are analyzed by considering internal pressures of power and sine functions, respectively. By comparing with the known methods, the observations reveal that a good approximation can be achieved using less derivative times, less discretization points, and a suitable weight parameter. The obtained results show that the crack growth is dependent on applied mechanical loadings.     

Multiple Scales via Galerkin Projections: Approximate Asymptotics for Strongly Nonlinear Oscillations

The method of multiple scales and the related method of averaging are commonly used tostudy slowly modulated oscillations. If the system of interest is a slightlyperturbed harmonic oscillator, then these techniques can be applied easily. If the unperturbed system is strongly nonlinear (though possiblyconservative), then these methods can run into difficulties due to the impossibilityof carrying out required analytical operations in closed form.In this paper, we abandon the requirement of closed form analyticaltreatment at all stages. Instead, Galerkin projections are used toobtain approximate realizations of the method of multiple scales. Thispaper adapts recent work using similar ideas for approximaterealizations of the method of averaging. A key contribution of thepresent work is in the systematic identification and removal of secularterms in the general nonlinear case, a procedure that is more difficultthan for the perturbed harmonic oscillator case, and that is unnecessaryfor averaging.A strength of the present work is that the heuristics (Galerkin)and asymptotics (multiple scales) are kept distinct,leaving room for systematic refinement of the formerwithout compromising the asymptotic features of the latter.     

橡胶基复合靶抗贯穿特性的近似分析方法

采用体积含量加权的方法确定了复合靶等效状态方程参数,采用纤维含量平方外推的方法确定了复合靶的等效强度。然后利用球腔膨胀和柱腔贯穿相结合的方法提出了一种分析计算钢球贯穿橡胶基复合靶的近似分析模型。计算方法简明、高效,而且对剩余速度和临界穿透速度等的计算结果与已有实验有良好的符合。     

Dewar瓶内液体晃动的近似计算方法

本文研究Dewar瓶内液体的晃动特征问题，将液体晃动的微分方程边值问题转换为具有积分形式的泛函极值问题，在此基础上建立了旋转对称容器液体晃动特征问题的有限元数值计算方法和通用程序，并计算了Dewar球，球腔，圆柱腔液体的晃动固有频率，结果显示了Dewar瓶综合了球腔和圆柱腔液体晃动的特征，它将液体晃动频率控制在一窄带范围之内。利用该程序，本文又计算了Dewar瓶液体晃动的单摆模型，为了便于工程应用，本文提出了一种对Dewar瓶建立等效圆柱容器液体晃动模型的方法，给出了模型的参数变换公式，从而可以通过对圆柱窝器液体晃动的解析计算得到Dewar瓶的液体晃动结果。利用数值计算结果，本文验算了近似计算方法的有效性和近似程序。     

Boussinesq方程的发展形式与Airy波理论差异性研究

应用势流理论，采用递推函数方法推导出一个新形式的Ｂｏｕｓｉｎｅｓｑ方程。通过对新方程的参数设置，可以讨论出Ｂｏｕｓｓｉｎｅｓｑ方程发展趋势和不同的发展形式。对浅水波动的描述方程，Ｂｏｕｓｓｉｎｅｓｑ方程的发展趋势为适用水深范围的拓展。拓展应用范围的大小则由其方程频散特征向Ａｉｒｙ波频散解逼近程度来决定。而Ｂｏｕｓｉｎｅｑ方程又不同于Ａｉｒｙ波，主要原因是Ｂｏｕｓｓｉｎｅｓｑ方程中含有线性频散项，Ａｉｒｙ波则只是长波首项近似，无线性频散项。其频散特征为精确的线性频散解。对实际水波传播而言，Ａｉｒｙ波理论的局限性是不言而喻的。     

Flow past an axisymmetric body embedded in a saturated porous mediumÉcoulement derrière un corps à symétrie axiale plongé dans un milieu poreux saturé

The problem of viscous fluid past an axisymmetric body embedded in a fluid saturated porous medium is studied using the Brinkman's extension. A general formula for the drag on the body is derived in the form of a limit of an expression involving the stream function characterizing the flow. The flow past an axisymmetric approximate sphere is also considered. The stream function in this case is obtained in terms of Bessel functions and Gegenbauer's functions. The drag acting on the body is evaluated by using the formula derived. Its variation is studied with respect to geometric and permeability parameters. The special cases of flow past a sphere and a spheroid are obtained from the present analysis. To cite this article: D. Srinivasa Charya, J.V. Ramana Murthy, C. R. Mecanique 330 (2002) 417–423.     

Computer algebra-perturbation solution to a nonlinear wave equation

In this paper, the higher-order asymptotic solution to the Cauchy problem of a nonlinear wave equation is found by using a computer algebra-perturbation method. The secular terms in the solution from straightforward expansions are eliminated with the straining of characteristic, coordinates and the use of the renormalization technique, and the four-term uniformly valid solution is obtained with the symbolic computation by using a computer algebra system. The comparison of the derived asymptotic solution and the numerical solution shows that they coincide with each other for smaller ε and agree quite well for larger ε (e. g., ε=0.25) Project supported by the National Natural Science Foundation of China and Shanghai Municiple Natural Science Foundation     

Approximate inertial manifolds for reaction-diffusion equations in high space dimension

The concept of approximate inertial manifolds was introduced by Foiaset al. (1987) in the case of the two-dimensional Navier-Stokes equations. These manifolds are finite dimensional smooth manifolds such that the orbits enter a very thin neighborhood of the manifold after a transient time; this concept replaces the one of inertial manifold when either an inertial manifold does not exist or its existence is not known. Our aim in this paper is to prove that approximate inertial manifolds exist for reaction-diffusion equations in high space dimension by opposition with exact inertial manifolds whose existence has only been proved in low dimension and for which nonexistence results have been obtained in space dimensionn=4.     

A defect correction approach to turbulence modeling

A method for resolving turbulent flow problems is presented, aiming at competing with the existing mathematical tractable Approximate Deconvolution Models in terms of accuracy, and outperforming these models in terms of the computational time needed. Full numerical analysis is performed, and the method is shown to be stable, easy to implement and parallelize, and computationally fast. The proposed method employs the defect correction approach to solve spatially filtered Navier–Stokes equations. A simple numerical test is provided that compares the method against the approximate deconvolution turbulence model (ADM). When resolving a fluid flow at high Reynolds number, the numerical example verifies the key feature of the method: while having the accuracy comparable to that of the ADM, the method computes in less than 80% of the time needed for the turbulence model—even before the parallelization.© 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 268–288, 2015