Outflow Boundary Conditions for the Fourier Transformed One-Dimensional Vlasov–Poisson System

In order to facilitate numerical simulations of plasma phenomena where kinetic processes are important, we have studied the technique of Fourier transforming the Vlasov equation analytically in the velocity space, and solving the resulting equation numerically. Special attention has been paid to the boundary conditions of the Fourier transformed system. By using outgoing wave boundary conditions in the Fourier transformed space, small-scale information in velocity space is carried outside the computational domain and is lost. Thereby the so-called recurrence phenomenon is reduced. This method is an alternative to using numerical dissipation or smoothing operators in velocity space. Different high-order methods are used for computing derivatives as well as for the time-stepping, leading to an over-all fourth-order method.     

一维抛物型方程的一个新的高精度显式差分格式

工程技术中,常常需要求解抛物型方程．一维情形下的模型问题为 用差分方法解上述问题,隐格式常因计算量很大而不便使用,构造稳定性好精度高的显格式是非常必要的．文山构造了求解Ｐ维抛物型方程的分支绝对稳定的显式差分格式,但格式的精度不高,截断误差仅为 ．本文就 p＝ １情形构造了一个解问题（１）－（３）的新的显格式,精度较文［１］有较大的提高,截断误差可达． §１．差分格式的构造 设△ｔＬ为时间步长,△ｘ= Ｌ／Ｍ（Ｍ为正整数）为空间步长,网函数ｕ（ｊ△ｘ,ｎ△ｔ）记为ｕｊｎ．对方程（１）建立如下的差分格式：其…     

解Hamilton-Jacobi方程的无振荡局部加密方法

０．引 言 近年来,Ｈａｍｉｌｔｏｎ－Ｊａｃｏｂｉ方程（简称Ｈ－Ｊ方程）的数学理论与数值逼近已引起人们越来越多的关注．Ｈ－Ｊ方程不仅在原有的领域例如控制论、微分几何等有非常重要的应用［８］,而且不断开拓新的应用领域,例如用于网格生成［５］以及流体界面的水平集方法计算 ［９,１２,１３,１５］等．由于 Ｈ－Ｊ方程解的导数会出现间断,导致解曲面（线）出现尖点或纽结等现象［７］,故如何做到既节省计算时间,又能在光滑区域高精度数值求解和较好地分辨间断是一个十分重要的问题．文卜］通过在每个坐标方向构造单变量的…     

二维Helmholtz方程外问题基于自然边界归化的重叠型区域分解算法

１．引 言 设是平面光滑闭曲线,是以为边界的外部区域,考虑二维Ｈｅｌｍｈｏｌｔｚ方程外Ｎｅｕｍａｎｎ问题并在无穷远处满足Ｓｏｍｍｅｒｆｅｌｄ辐射条件其中是区域的边界的外法线方向,即指向由包围的内部区域．κ在许多情况下（例如约化波动方程）是实数,在另一些情况下则是纯虚数．本文仅讨论κ为纯虚数的情况,且不失一般性,可设Ｉｍ（ｋ）＞０． 用某些数值方法求解线性抛物型方程或线性双曲型方程的初边值问题时,可能导致求解Ｈｅｌｍｈｏｌｔｚ方程的外问题．例如,用自然边界元法求解线性抛物型方程的初边值问题时就导致求…     

周期黎卡提微分方程正定解的存在性

讨论了标准的周期黎卡提微分方程,给出了其存在埃尔米特周期正定（HPPD）解的一个完整的充分必要条件。准确地说,在经过一个适当的状态空间基底变换后该条件通过能稳性和能检测性概念表述。结果表明,当HP－PD解存在时,它或者是唯一的,或者有无限多个。这一结果可以看作是Richardson和Kwong的结果对周期时变情况的扩展。     

Surface tension calculation of the Sn–Ga–In ternary alloy

Surface tensions of the Sn–Ga–In ternary alloy are calculated from the surface tensions of the Sn–Ga, Ga–In and In–Sn sub-binary systems by using geometric models (the Kohler model and the Toop model), and a general solution model (the Chou model). The calculated results are in excellent agreement with the experimental data (except for the Kohler model), assuming an experimental accuracy of ±2.5%. At the same time, the surface tensions of the Sn–Ga–In ternary alloy at 773 K and their sub-binary systems are predicted on the basis of Butler’s equation, in combination with thermodynamic data, and different model parameters β$\beta$ equal to the ratio of the coordination number in the surface phase to that in the bulk phase. Different values of β$\beta$ have almost no influence on the surface tensions. The predicted results agree with the experimental data. Therefore, the resulting iso-surface tension curves for the Sn–Ga–In ternary alloy at 773 K, especially those calculated by using the Toop model, are reasonable.     

The periodic nature of the positive solutions of a nonlinear fuzzy max-difference equation

We investigate the periodic nature of the positive solutions of the fuzzy difference equation , where k, m are positive integers, A₀, A₁, are positive fuzzy numbers and the initial values x_i, i = −d, −d + 1, … , −1, d = max{k, m}, are positive fuzzy numbers. In addition, we give conditions so that the solutions of this equation are unbounded.     

On the analysis of stochastic divide and conquer algorithms

This paper develops general tools for the analysis of stochastic divide and conquer algorithms. We concentrate on the average performance and the distribution of the running time of the algorithm. As a special example we analyse the average performance and the running time distribution of the (2k + 1)-median version of Quicksort. Online publication October 13, 2000.     

不满足匹配条件的非确定性系统的鲁棒滑模控制

针对一类非确定性时变系统实施滑模控制,该系统在状态矩阵和控制输入矩阵中都 包含不满足匹配条件的不确定项.给出了能使系统鲁棒镇定的切换面设计方法和相应的控制 律的形式.同时,也给出了系统渐近稳定的充分条件.设计过程中的代数黎卡提方程和线性矩 阵不等式形式简单,易于求解.仿真结果证明了理论的正确性.     

高雷诺数流动的平均化差分格式

本文在N—S方程涡量一流函数形式的经典ADI格式和SOR松驰迭代公式的基础上,对其“外来项”进行平均化处理,构造出了平均化差分格式及迭代求解程序。对雷诺数Re=100,1000,10000的空腔流动分别进行了数值计算,并与各数值方法的结果及实验资料进行了比较,结果令人满意。