不可微预报系统的广义变分同化方法及数值试验

讨论了不可微预报系统中的广义变分同化方法．对于不可微预报系统,由于不可微性,系统不存在切线性系统,而切线性系统的不存在,使得无法用通常的途径导出伴随系统A·D2引进不可微系统的弱形式后,可以不考虑切线性系统,而直接导出伴随系统．主要就3种形式的问题展开了讨论,第1种为低维系统,第2种情形为高维系统整体观测资料,第3种情形为高维系统局部观测资料．可以称此方法为结合反问题思想的广义变分同化方法．     

论带有趋势变化的变量的相关:数值试验

当计算相关的二个变量都包含有明显的趋势变化成分时,原变量之间的相关特征可能被歪曲(夸大或者缩小).对此问题进行了数值试验,结果表明,变量带有性质相反的趋势变化,会使这二个变量之间的相关系数减小(正相关的数值减小,负相关被夸大).变量带有性质相同的趋势变化,会使这二个变量之间的相关系数增加(正相关被夸大,负相关数值变小).数值试验还表明,趋势变化对相关的影响具有可交换性.只要不改变它们趋势变化的数值,它们叠加的变量互相交换,影响相关系数的后果是一样的;研究还指出,二个变量有相同的变化趋势时,对相关的影响会更大些.给出了实例.     

Numerical Experiment for Stabilization of the Heat Equation by Dirichlet Boundary Control

We use the boundary feedback control introduced in Barbu [Boundary stabilization of equilibrium solutions to parabolic equations, IEEE Trans. Automat. Control (accepted)], in order to stabilize an unstable heat equation in two dimensions. We propose two numerical algorithms. The feedback boundary condition is treated explicitly in the first algorithm. At each time step, only one linear system is solved. The second algorithm performs at each time step some subiterations, in order to treat the feedback boundary condition implicitly. The second algorithm can stabilize some problems where the first algorithm fails.     

血流动力学模型及应用研究

针对现有血流模拟中采用的流体动力学模型计算量大且实时性差的问题,采用不可压缩稳态非牛顿流体模型对血液流动现象进行仿真,提出一种改进的血流模拟数值计算方法.首先根据血液流变性质、仿真的实时性与细节性的要求,选取合适的血流动力学模型;然后根据所选取的动力学模型,对现有的离散方法进行一定的改进,使得离散后方程的计算量符合仿真的实时性要求;最终计算出粒子的运动信息.实验证明,算法能够有效地降低血流数值计算的复杂度,提高血流绘制的效率.     

浅水方程初边值问题几种新的差分格式及其数值试验

本文提出几种有限差分法求解绝对坐标系中浅水方程的新方法;对五个对角线矩阵也提出了效率高而且简单的两级迭代计算的有效方法.这种迭代法可以用来处理浅水方法的多格计算.最后我们研究了初始边界值问题.通过数值试验证明,线性正弦波会逐步变为非线性的圆锥型波.     

血液动力学中血管流激波与驻波的相互作用

血液动力学问题是生物力学心血管系统中的重要研究课题.血管内斑块处,血管截面和血管壁的材质发生变化,对血液流动产生重要影响.血液流动中基本波及其相互作用对探究血液流动的规律、生理学意义及与疾病的关系有着重要的意义.本文研究血液动力学血液流动简化数学模型的基本波的相互作用.血管流模型是3×3非严格双曲型方程组.构造性地得到了初值为三段常状态时,血管流问题的解,即解决了激波与驻波的相互作用问题.特别地,给出四种后前激波与驻波的相互作用的结果.     

An Explanation of the Non‐unique Behaviour of a Textile Probe in the Drape Experiment ‐ Numerical Stability Analysis

The paper proves, that the ambiguous behaviour of a textile probe in the drape experiment is connected with many possible equilibrium states. This experiment is usually used for the evaluation of the drapeability of textiles. We treat a textile surface in our mathematical model as a two‐dimensional Cosserat continuum, which equilibrium equations can be easily formulated. To solve the boundary value problem, which assures equilibrium, we use the finite element method in connection with the arc‐length method. This strategy allows us to trace the highly non‐linear behaviour of the system. This nonlinearity is responsible for the non‐unique behaviour of a textile probe in drape. In our investigation we calculate some of the possible final configurations of a round textile probe supported on the round table. Such configurations can be observed in the drape experiment.     

An Experiment in Problem Formulation

In a recent paper (in Operational Research '81, North-Holland, 1981), the author put forward a methodology for problem-formulation. In order to test it, a group of teachers concerned with the introduction of a new, integrated operational research and systems analysis M.Sc. course agreed to accept the author as a consultant. The aim was to clarify and define their problem of developing and maintaining their new course. This paper describes the nature and course of the experiment. It comments on the difficulties that were encountered, and on the perceived benefits to the client-group and to the researcher.     

Numerical ranges in physics

Some examples of the incidence of Numerical Ranges in Physics are discussed. The Thermodynamical Inequality is deduced using the theory of Numerical Ranges. The Peierls-Bogoliubov inequality is obtained from the Thermodynamical Inequality. The formalism of Thermo Field Dynamics is summarized in the same framework.     

数学实验在工程数学教学中的应用

从《工程数学》教学实践出发,针对当前面临的教与学困难,提出引进《数学实验》课以解决这一问题.阐述了《数学实验》课的特点、重要性、作用,并给出具体实施办法.《数学实验》课可全方位提高学生学习《工程数学》兴趣,进而提高应用《工程数学》解决问题的能力.     

Positive Bases in Numerical Optimization

The theory of positive bases introduced by C. Davis in 1954 does not appear in most modern texts on linear algebra but has re-emerged in publications in optimization journals. In this paper some simple properties of this highly useful theory are highlighted and applied to both theoretical and practical aspects of the design and implementation of numerical algorithms for nonlinear optimization.     

Numerical experiments in semi-infinite programming

A quasi-Newton algorithm for semi-infinite programming using an L exact penalty function is described, and numerical results are presented. Comparisons with three Newton algorithms and one other quasi-Newton algorithm show that the algorithm is very promising in practice.     

Error Propagation in Numerical Processes

A method is suggested of analysing the mechanism of error propagationin certain numerical processes, and detailed results are obtainedfor the solution of triangular linear systems, polynomial deflation,LU decomposition and matrix reduction to tridiagonal form usingHouseholder transformations. The analysis is also applicableto the solution of ordinary differential equations.     

Numerical method in wave-body interactions

The application of Green's function in calculation of flow characteristics around submerged and floating bodies due to a regular wave is presented. It is assumed that the fluid is homogeneous, inviscid and incompressible, the flow is irrotational and all body motions are small. Two methods based on the boundary integral equation method (BIEM) are applied to solve associated problems. The first is a low order panel method with triangular flat patches and uniform distribution of velocity potential on each panel. The second method is a high order panel method in which the kernels of the integral equations are modified to make it nonsingular and amenable to solution by the Gaussian quadrature formula. The calculations are performed on a submerged sphere and some floating spheroids of different aspect ratios. The excellent level of agreement with the analytical solutions shows that the second method is more accurate and reliable.     

Best Approximation in Numerical Radius

Let X be a reflexive Banach space. In this article, we give a necessary and sufficient condition for an operator T ∈ 𝒦(X) to have the best approximation in numerical radius from the convex subset 𝒰 ? 𝒦(X), where 𝒦(X) denotes the set of all linear, compact operators from X into X. We also present an application to minimal extensions with respect to the numerical radius. In particular, some results on best approximation in norm are generalized to the case of the numerical radius.     

The Elicited Progressive Decoupling Algorithm: A Note on the Rate of Convergence and a Preliminary Numerical Experiment on the Choice of Parameters

Set-Valued and Variational Analysis - The paper studies the progressive decoupling algorithm (PDA) of Rockafellar and focuses on the elicited version of the algorithm. Based on a generalized...