A CLASS OF r-POINT (r+1)ST-ORDER A-STABLE ONE-BLOCK METHODS WITH DAMPING AT THE INFINITE POINT

1　ＩｎｔｒｏｄｕｃｔｉｏｎＦｏｒｓｏｌｖｉｎｇｓｔｉｆｆｉｎｉｔｉａｌｖａｌｕｅｐｒｏｂｌｅｍｓｆｏｒｓｙｓｔｅｍｓｏｆＯＤＥｓｙ′=ｆ(ｙ) ,ｙ(ｔ0 ) =ｙ0 ,ｔ0 <ｔ≤Ｔ ,ｙ0 ,ｙ∈Ｒｍ,ｆ :Ω Ｒｍ →Ｒｍ (1 .1 )ｍａｎｙｐａｒｔｉｃｕｌａｒｏｎｅ ｂｌｏｃｋｍｅｔｈｏｄｓｏｆｔｈｅｆｏｒｍＹｎ+1= ＡＹｎ+ｈ( Ｂ0 Ｆ(Ｙｎ) + Ｂ1Ｆ(Ｙｎ+1) ) , Ａ =Ａ Ｉｍ, Ｂｉ=Ｂｉ Ｉｍ,Ａ ,Ｂｉ∈Ｒｒ×ｒ,Ｙｎ =(ＹＴｎｒ,… ,ｙＴ(ｎ+1)ｒ- 1) Ｔ,Ｆ(Ｙｎ) =(ｆＴ(ｙｎｒ) ,… ,ｆＴ(ｙ(ｎ+1)ｒ- 1) ) Ｔ,ｙｊ≈ ｙ(ｔｊ) ,…     

Extension of a combined analytical/numerical initial value problem solver for unsteady periodic flow

Here we describe analytical and numerical modifications that extend the Differential Reduced Ejector/ mixer Analysis (DREA), a combined analytical/numerical, multiple species ejector/mixing code developed for preliminary design applications, to apply to periodic unsteady flow. An unsteady periodic flow modelling capability opens a range of pertinent simulation problems including pulse detonation engines (PDE), internal combustion engine ICE applications, mixing enhancement and more fundamental fluid dynamic unsteadiness, e.g. fan instability/vortex shedding problems. Although mapping between steady and periodic forms for a scalar equation is a classical problem in applied mathematics, we will show that extension to systems of equations and, moreover, problems with complex initial conditions are more challenging. Additionally, the inherent large gradient initial condition singularities that are characteristic of mixing flows and that have greatly influenced the DREA code formulation, place considerable limitations on the use of numerical solution methods. Fortunately, using the combined analytical–numerical form of the DREA formulation, a successful formulation is developed and described. Comparison of this method with experimental measurements for jet flows with excitation shows reasonable agreement with the simulation. Other flow fields are presented to demonstrate the capabilities of the model. As such, we demonstrate that unsteady periodic effects can be included within the simple, efficient, coarse grid DREA implementation that has been the original intent of the DREA development effort, namely, to provide a viable tool where more complex and expensive models are inappropriate. Copyright © 2002 John Wiley & Sons, Ltd.     

进一步改进边界元方法以克服振动声辐射计算中解的非唯一性

章利用基于三次B样条插值的边界元方法，对振动体外部声辐射问题进行了研究，对CHIEF法及其改进方法作了进一步的改进，提出在加权余量意义下，通过把内部Helmholtz积分方程与其对内点坐标取导后的方程式作线性叠加，在域外构作的一个小体积块上进行积分以形成补充方程，经与表面Helmholtz积分方程相结合，来求解任意频率下的声辐射问题，并以脉动球和摆动球作为算例，说明本提出的方法能够有效地克服在特殊频率处解的非唯一性问题。     

变量有广义界线性规划的直接对偶单纯形法

本文讨论变量有广义界线性规划问题借助标准形线性规划同单纯形法技术，建立问题的一个直接对偶单纯形法。分析了方法的性质，给出了初始对偶可行基的计算方法，并用实例说明方法的具体操作。     

溶胶-凝胶VO2薄膜转换特性研究

利用溶胶凝胶法在SiO2Si衬底上沉积高取向的V2O5薄膜,在压强低于2Pa,温度高于400℃的条件下,对V2O5薄膜进行真空烘烤,获得了电阻率变化3个数量级以上、弛豫宽度为62℃的VO2多晶薄膜.以X射线衍射(XRD)、扫描电子显微镜(SEM)图和电阻率转换特性等实验结果为依据,详细分析了溶胶凝胶薄膜在真空烘烤时从V2O5向VO2的转化,它经历了从VnO2n+1(n=2,3,4,6)到VO2的过程.实验证明,根据选择合适的成膜热处理条件和真空烘烤条件是实现溶胶凝胶V2O5结构向VO2结构成功转换的关键 关键词： 溶胶-凝胶法 氧化钒薄膜 VO2膜转换特性     

A marker method for the solution of the damped Burgers' equation

A new method for the solution of the damped Burgers' equation is described. The marker method relies on the definition of a convective field associated with the underlying partial differential equation; the information about the approximate solution is associated with the response of an ensemble of markers to this convective field. Some key aspects of the method, such as the selection of the shape function and the initial loading, are discussed in some details. The marker method is applicable to a general class of nonlinear dispersive partial differential equations. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

Approximation of Matrices and a Family of Gander Methods for Polar Decomposition

Two matrix approximation problems are considered: approximation of a rectangular complex matrix by subunitary matrices with respect to unitarily invariant norms and a minimal rank approximation with respect to the spectral norm. A characterization of a subunitary approximant of a square matrix with respect to the Schatten norms, given by Maher, is extended to the case of rectangular matrices and arbitrary unitarily invariant norms. Iterative methods, based on the family of Gander methods and on Higham’s scaled method for polar decomposition of a matrix, are proposed for computing subunitary and minimal rank approximants. Properties of Gander methods are investigated in details. AMS subject classification (2000) 65F30, 15A18     

大规模界约束优化的子空间截断牛顿法

给出了大规模界约束优化的一个子空间截断牛顿法。利用截断牛顿法修正非有效约束所对应的变量，用投影梯度法修正有效约束所对应的变量，文中证明了方法的整体收敛性，并对方法进行了数值试验，且与子空间有限内存拟牛顿法进行了数值比较。     

用区域分解算法结合蒙特卡罗法求坦克温度场和红外辐射出射度

本文将区域分解算法和蒙特卡罗法相结合，求坦克温度场和红外辐射出射度．采用蒙特卡罗法计算辐射传递系数，可以考虑界面的复杂辐射特性，如：镜反射、各向异性发射、各向异性反射等；可直接考虑界面的复杂几何特性，如:相互遮挡、太阳入射方向上的投影面积等．引入辐射传递系数，分离了计算的难点，使得在时间域（计算步骤）上能把整个问题分解为若干个子问题并行处理、在空间域（计算区域）上将坦克分解为若干个子区域，缩小计算规模，并可使用多个处理器并行计算；同时减轻了蒙特卡罗法编程的难度，缩短了计算时间．     

泊松类型方程边界元解法

本文采用高阶拉普拉斯算子基本解将泊松类型方程的区域积分全部变换成边界积分，使计算问题的维数减少一维．通过斯托克斯方程的算例，表明本文所用的方法是有效的方法。