Recursive super-convergence computation for multi-dimensional problems via one-dimensional element energy pro jection technique

This paper presents a strategy for computation of super-convergent solutions of multi-dimensional problems in the finite element method （FEM） by recursive application of the one-dimensional （1D） element energy projection （EEP） technique. The main idea is to conceptually treat multi-dimensional problems as generalized 1D problems, based on which the concepts of generalized 1D FEM and its consequent EEP formulae have been developed in a unified manner. Equipped with these concepts, multi-dimensional problems can be recursively discretized in one dimension at each step, until a fully discretized standard finite element （FE） model is reached. This conceptual dimension-by- dimension （D-by-D） discretization procedure is entirely equivalent to a full FE discretization. As a reverse D-by-D recovery procedure, by using the unified EEP formulae together with proper extraction of the generalized nodal solutions, super-convergent displacements and first derivatives for two-dimensional （2D） and three-dimensional （3D） problems can be obtained over the domain. Numerical examples of 3D Poisson＇s equation and elasticity problem are given to verify the feasibility and effectiveness of the proposed strategy.

Solution Method for Singular Initial Value Problems of One-dimensional Steady Transonic Flow in a Dual-mode Scramjet

Singular initial value problems arise in solving one-dimensional steady transonic flow of dualmode scramjet. The existing solution method has the problems of large initial value errors in principles. This paper puts forward an improved algorithm based on variable transformation, and constructs a nonsingular one-dimensional steady transonic flow equation by defining a new variable. The improved algorithm can eliminate the singularity of the differential equation, and can solve the singular initial value problems of one-dimensional steady transonic flow of dual-mode scramjet.

Existence Results for m-Point Boundary Value Problem at Resonance with One-dimensional p-Laplacian

By using Mawhin＇s continuation theorem, the existence of a solution for a class of m-point boundary value problem at resonance with one-dimensional p-Laplacian is obtained. An example is given to demonstrate the main result of this paper.

Explicit One-Step P-Stable Methods for Second Order Periodic Initial Value Problems

In this paper, we present an explicit one-step method for solving periodic initial value problems of second order ordinary differential equations. The method is P-stable, and of first algebraic order and high phase-lag order. To improve the algebraic order, we give a composition second order scheme with the proposed method and its adjoint. We report some numerical results to illustrate the efficiency of our methods.

On the Stable Method Computing Values of Unbounded Operators

Unbounded operators can transform arbitrarily small vectors into arbitrarily large vectors—a phenomenon known as instability. Stabilization methods strive to approximate a value of an unbounded operator by applying a family of bounded operators to rough approximate data that do not necessarily lie within the domain of unbounded operator. In this paper we shall be concerned with the stable method of computing values of unbounded operators having perturbations and the stability is established for this method.

On the Stable Sequential Kuhn-Tucker Theorem and Its Applications

The Kuhn-Tucker theorem in nondifferential form is a well-known classical optimality criterion for a convex programming problems which is true for a convex problem in the case when a Kuhn-Tucker vector exists. It is natural to extract two features connected with the classical theorem. The first of them consists in its possible “impracticability” (the Kuhn-Tucker vector does not exist). The second feature is connected with possible “instability” of the classical theorem with respect to the errors in the initial data. The article deals with the so-called regularized Kuhn-Tucker theorem in nondifferential sequential form which contains its classical analogue. A proof of the regularized theorem is based on the dual regularization method. This theorem is an assertion without regularity assumptions in terms of minimizing sequences about possibility of approximation of the solution of the convex programming problem by minimizers of its regular Lagrangian, that are constructively generated by means of the dual regularization method. The major distinctive property of the regularized Kuhn-Tucker theorem consists that it is free from two lacks of its classical analogue specified above. The last circumstance opens possibilities of its application for solving various ill-posed problems of optimization, optimal control, inverse problems.

浅析羊肚菌稳产高产相关的科学技术问题

六妹羊肚菌(Morchella sextelata)、梯棱羊肚菌(M.importuna)和七妹羊肚菌(M.eximia)在我国已经实现商业化栽培,但依然无法稳产高产。笔者明确指出羊肚菌栽培面临的风险,剖析羊肚菌在遗传多样性、性亲和模式与生活史、菌核及菌霜生物学功能、营养吸收与转运机制、环境作用机制等方面需要研究的基本科学问题,明确羊肚菌在菌种质量管理、栽培场地适宜性评价、生长环境调控、田间精细管理等方面亟待突破的技术难题,阐述羊肚菌稳产高产栽培理论及关键技术的研究方向和目标。

空分高压液氧泵运行优化探析

简介液氧泵的配置,详细分析了液氧泵运行中存在的问题,针对液氧泵运行的问题进行优化改进,简述了液氧泵启动以及运行中注意事项,确保液氧泵长周期稳定运行。

New hybrid FDTD algorithm for electromagnetic problem analysis

Since the time step of the traditional finite-difference time-domain(FDTD) method is limited by the small grid size, it is inefficient when dealing with the electromagnetic problems of multi-scale structures.Therefore, the explicit and unconditionally stable FDTD(US-FDTD) approach has been developed to break through the limitation of Courant–Friedrich–Levy(CFL) condition.However, the eigenvalues and eigenvectors of the system matrix must be calculated before the time iteration in the explicit US-FDTD.Moreover, the eigenvalue decomposition is also time consuming, especially for complex electromagnetic problems in practical application.In addition, compared with the traditional FDTD method, the explicit US-FDTD method is more difficult to introduce the absorbing boundary and plane wave.To solve the drawbacks of the traditional FDTD and the explicit US-FDTD, a new hybrid FDTD algorithm is proposed in this paper.This combines the explicit US-FDTD with the traditional FDTD, which not only overcomes the limitation of CFL condition but also reduces the system matrix dimension, and introduces the plane wave and the perfectly matched layer(PML) absorption boundary conveniently.With the hybrid algorithm, the calculation of the eigenvalues is only required in the fine mesh region and adjacent coarse mesh region.Therefore, the calculation efficiency is greatly enhanced.Furthermore, the plane wave and the absorption boundary introduction of the traditional FDTD method can be directly utilized.Numerical results demonstrate the effectiveness, accuracy, stability, and convenience of this hybrid algorithm.

Stability problem in Rindler spacetime

The stability problem of the Rindler spacetime is carefully studies by using the scalar wave perturbation. Using two different coordinate systems, the scalar wave equation is investigated. The results are different in the two cases. They are analysed and compared with each other in detail. The following conclusions are obtained： （a） the Rindler spacetime as a whole is not stable; （b） the Rindler spacetime can exist stably only as part of the Minkowski spacetime, and the Minkowski spacetime can be a real entity independently; （c） there are some defects for the scalar wave equation written by the Rindler coordinates, and it is unsuitable for the investigation of the stability properties of the Rindler spacetime. All these results may shed some light on the stability properties of the Schwarzschild black hole. It is natural and reasonable for one to infer that： （a） perhaps the Regge-Wheeler equation is not sufficient to determine the stable properties; （b） the Schwarzschild black hole as a whole might be really unstable; （c） the Kruskal spacetime is stable and can exist as a real physical entity; whereas the Schwarzschild black hole can occur only as part of the Kruskal spacetime.

CHEBYSHEV PSEUDOSPECTRAL DOMAIN DECOMPOSITION METHOD OF ONE－DIMENSIONAL ELLIPTIC PROBLEMS

This paper is devoted to the Chebyshev pseudospectral domain decomposition method of one-dimensional elliptic problems,it is easily applied to complex geometry.The approximate accuracy can be increased by increasing the order of approximation in fixed number of subdomains,rather than by resorting to a further partitioning.The stability and the convergence of this method are proved.

电解海水制氯稳定运行方案研究

河北某公司自备电站采用海水作为循环冷却水源,为了抑制冷却水中藻类及细菌微生物的大量繁殖,保障机组安全运行,电解制氯装置需全年投入运行。文章分析了电解海水制氯系统全年运行存在的问题,并讨论了解决措施,提出了改造方案及改造期间的保障措施。

浅水波方程熵稳定格式的保平衡性

保平衡性是浅水波方程的一个重要性质,满足保平衡性的格式理论上能够准确捕捉稳态的微小扰动.针对带有底部地形源项的浅水波方程设计恰当的数值耗散算子并选择合适的源项离散方式以精确平衡非零通量与源项,构造了一类保平衡的高阶熵稳定格式,提出了高阶熵守恒格式以及熵稳定格式的保平衡性定理并给予理论证明.利用新格式计算几个典型的数值算例,数值结果表明新格式能够很好地处理稳态解的小扰动问题.

基于大幅值Lyapunov轨道稳定流形的地月转移方法

针对现有的基于不变流形地月转移轨道设计方法存在的转移时间长、需要额外速度增量的缺点,本文利用平面圆型限制性三体问题下大幅值Lyapunov轨道的稳定流形,提出了一种地月低能转移轨道设计方法。首先计算与给定近月轨道相切的大幅值Lyapunov轨道作为参考轨道;然后根据小偏差值对稳定流形的影响确定Lyapunov轨道初始点的取值范围;再通过最近点截面确定与给定近地轨道相切的Lyapunov轨道的稳定流形;最后根据稳定流形的切点调整近月轨道半径,通过一条稳定流形直接连接近地轨道与近月轨道来实现地月转移。仿真结果表明,该方法仅需要两次速度增量,在能耗较低的前提下大大减少了探测器渐近Lyapunov轨道时的飞行时间,为地月低能转移轨道的设计提供了一种新思路。

Inverse Piston Problem for the System of One-Dimensional Isentropic Flow

In this paper, the authors consider the inverse piston problem for the system of one-dimensional isentropic flow and obtain that, under suitable conditions, the piston velocity can be uniquely determined by the initial state of the gas on the right side of the piston and the position of the forward shock.

MULTIPLICITY OF POSITIVE SOLUTIONS TO MULTIPOINT BOUNDARY VALUE PROBLEM WITH ONE-DIMENSIONAL p-LAPLACIAN

In this paper, we consider a multipoint boundary value problem for one-dimensional p-Laplacian. Using a fixed point theorem due to Bai and Ge, we study the existence of at least three positive solutions to the boundary value problem. In this problem, the nonlinear term explicitly involves a first-order derivative, which is different from some previous ones.

不同矢跨比倒放四角锥立体拱桁架结构稳定分析

利用有限元分析软件MIDAS建立了一跨度50m的立体拱桁架结构模型,分析了在矢跨比分别为1/4、1/5、1/6、1/7的承载力、变形。从分析结果可以得出:矢跨比越小桁架端部水平推力越大,对下部结构的承载力和变形要求越高,矢跨比越大反之,但拱桁架本身的稳定问题变得重要,实际工程中应结合空间需求选用合适的矢高比。还进行了不同失跨比下以结构的第一屈曲模态为初始缺陷的几何非线性稳定分析,得到不同失跨比下的临界荷载系数。

A Simulation Approach to the Stable Marriages Problem

The stable marriage problem stands for a class of assignment problems and has been attracting high attention from operational research community. Various versions of the problem and corresponding algorithms have been published. This paper introduces the characteristics of GPMS in object\|oriented simulation modelling through constructing a simulation model of the problem.

INVERSE SCATTERING PROBLEM FOR ONE-DIMENSIONAL SCHRDINGER OPERATORS RELATED TO THE GENERAL STARK EFFECT

This paper disccusses the inverse scattering problem for one-dimensional Schrodinger operatorsrelated to the general Stark effect. We provide a ganeral framework which can be applied both to theStark-effect operator and the ordinary Schrodinger operator.

SOLVABILITY FOR m-POINT BOUNDARY VALUE PROBLEM AT RESONANCE WITH ONE-DIMENSIONAL p-LAPLACIAN

By using Mawhin＇s continuation theorem, the existence of solution for a class of m-point boundary value problem at resonance with one-dimensional p-Laplacian is obtained. An example is given to demonstrate the main result of the paper.