一类四阶微积分方程的Legendre-Galerkin谱逼近

针对研究吊桥模型而建立的四阶微积分方程, 提出Legendre谱逼近法进行求解.构造迭代算法来求解得到的线性系统, 证明了迭代格式的收敛性, 对问题进行了误差分析.数值算例验证了迭代的收敛性和方法的高精度.     

基于卷积神经网络模型数值求解双曲型偏微分方程的研究

人工神经网络近年来得到了快速发展,将此方法应用于数值求解偏微分方程是学者们关注的热点问题.相比于传统方法其具有应用范围广泛（即同一种模型可用于求解多种类型方程）、网格剖分条件要求低等优势,并且能够利用训练好的模型直接计算区域中任意点的数值.该文基于卷积神经网络模型,对传统有限体积法格式中的权重系数进行优化,以得到在粗粒度网格下具有较高精度的新数值格式,从而更适用于复杂问题的求解.该网络模型可以准确、有效地求解Burgers方程和level set方程,数值结果稳定,且具有较高数值精度.     

边界节点法计算二维瞬态热传导问题

采用边界节点法(BKM)结合双重互易法(DRM)求解二维瞬态热传导问题.采用差分格式处理时间变量,可将原瞬态热传导方程转化为一系列非齐次修正的Helmholtz方程.随后,方程的解可分为特解和齐次解两部分计算,引入双重互易法在区域内部配点求解方程的特解,采用边界节点法仅需边界配点求解方程的齐次解.给出的数值算例显示该方法计算精度高,适用性好,具有很好的稳定性和收敛性,适合求解瞬态热传导问题.     

有限差分-配点法求解二维Burgers方程

将重心插值配点法结合Crank-Nicolson差分格式来求解Burgers方程.首先,利用Hopf-Cole变换将Burgers方程转化为线性热传导方程;空间方向采用重心插值配点法进行离散,时间方向采用Crank-Nicolson格式离散,导出对应的线性代数方程组,并对此计算格式进行相容性分析;最后,通过数值算例验证此计算格式具有高精度和有效性.     

覆冰导线舞动非线性数值模拟方法

基于覆冰导线所受空气动力的非线性和导线大幅运动的几何非线性,利用虚功原理建立覆冰导线非线性运动方程,采用具有3个平动自由度和1个扭转自由度的三结点等参单元,得到基于更新Lagmnge格式的覆冰导线的非线性动力学有限元方程.采用Newmark时间积分和Newton-Raphson非线性迭代法求解有限元方程.编制了相应的计算程序,利用算例验证了方法和程序的正确性.进而利用该方法通过对典型覆冰线路的数值模拟.揭示了当覆冰线路在垂直和水平方向固有频率之间存在整数倍关系的情况下,可能出现的一种新的舞动模式,其可理解为非线性动力系统的饱和现象.     

一维气液两相漂移模型全隐式AUSMV算法研究

气液两相漂移模型显式AUSMV（advection upstream splitting method combined with flux vector splitting method）算法的时间步长受限于CFL（Courant-Friedrichs-Lewy）条件，为了提高计算效率，建立了一种全隐式AUSMV算法求解气液两相漂移模型.采用AUSM格式结合FVS（flux vector splitting）格式构造连续方程和运动方程的对流项数值通量，AUSM格式构造压力项数值通量.离散控制方程是非线性方程组，采用六阶Newton(牛顿)法结合数值Jacobi矩阵求解.计算经典算例Zuber-Findlay激波管问题和复杂漂移关系变质量流动问题，结果分析表明:全隐式AUSMV算法，色散效应小，无数值震荡，计算精度高.在压力波波速高的条件下，可以显著提高计算效率，耗散效应小.     

钝体绕流非定常解

本文结合目前流场显示的研究课题,对方块物体和山形物体的钝体绕流在起动阶段的运动情况,进行相应的数值模拟.并用有限差分方法求解二维不可压缩流体运动的N-S方程的非定常解.对差分格式中的显式,隐式和交替方向隐式几种格式进行了讨论.最后用显式和交替方向隐式方法计算了山形物体和方块物体在起动阶段的运动情况.     

一种抑制激波计算中数值振荡现象的双重小波收缩方法

在激波数值计算中,容易出现数值振荡的问题,振荡激烈时会掩盖真实解,为此提出了许多高精度复杂计算格式或采用人工粘性抑制数值振荡.从信号处理的角度,提出双重小波收缩方法,它能自适应提取激波数值振荡解中的真实物理解.先用局部微分求积法求解浅水波方程和理想流体Euler运动方程中的激波问题,发现其数值振荡现象严重,然后采用双重小波收缩方法对其处理,获得了无数值振荡解,它能准确捕捉激波的位置并且保持激波结构.相比于复杂的Riemann(黎曼)求解格式,借助小波收缩方法,可以采用相对简单的计算格式如微分求积法求解激波问题.     

一维电磁波方程的四阶紧致差分格式

本文建立求解一维电磁波方程的四阶紧致差分格式,运用von Neumann法给出方法的稳定条件.运用能量法证明格式的收敛性.最后,数值例子验证了格式的有效性.     

张力腿平台有限振幅运动的方程和数值解

论证了张力腿平台（TLP）在波浪作用下发生有限振幅运动时,所受惯性力、粘性力、浮力等载荷不仅与波浪场有关,还与瞬时响应有关,是响应的非线性函数;张力腿拉力也是各自由度位移的非线性函数．所以分析TLP受力时必须考虑平台的瞬时加速度、速度和位移,在瞬时位置建立运动方程．据此推导出TLP发生有限振幅运动时的外力计算公式,建立了TLP 6自由度有限振幅运动非线性控制方程．其中考虑了由6自由度有限位移引起的多种非线性因素,如各自由度之间的耦合、瞬时湿表面、瞬时位置等;还包括自由表面效应、粘性力等因素引起的非线性．用数值方法求解所得到的非线性运动方程．对典型平台ISSC TLP进行了数值分析,求得该平台在规则波作用下的6自由度运动响应．用退化到线性范围的解与已有解进行了对比,吻合良好．数值结果表明,综合考虑非线性因素后响应有明显改变．     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.     

Towards Excellence in Science Chinese Academy of Sciences

<正>May 26,2014,Beijing Science is a human enterprise in the pursuit of knowledge.The scientific revolution that occurred in the 17th Century initiated the advances of modern science.The scientific knowledge system created by     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

<正>August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

Bounds for the zeros of polynomials

Let P(z)=∑↓j=0↑n ajx^j be a polynomial of degree n. In this paper we prove a more general result which interalia improves upon the bounds of a class of polynomials. We also prove a result which includes some extensions and generalizations of Enestrǒm-Kakeya theorem.     

Boundedness of commutators related to Marcinkiewicz integrals on hardy type spaces

In this paper, the authors study the boundedness of the operator [μΩ, b], the commutator generated by a function b ∈ Lipβ(Rn)(0 ＜β≤ 1) and the Marcinkiewicz integrals μΩ, on the classical Hardy spaces and the Herz-type Hardy spaces in the case Ω∈ Lipα(Sn-1)(0 ＜α≤ 1).     

Generalization of the interaction between Haar approximation and polynomial operators to higher order methods

In applications it is useful to compute the local average empirical statistics on u. A very simple relation exists when of a function f（u） of an input u from the local averages are given by a Haar approximation. The question is to know if it holds for higher order approximation methods. To do so, it is necessary to use approximate product operators defined over linear approximation spaces. These products are characterized by a Strang and Fix like condition. An explicit construction of these product operators is exhibited for piecewise polynomial functions, using Hermite interpolation. The averaging relation which holds for the Haar approximation is then recovered when the product is defined by a two point Hermite interpolation.     

Jacobi polynomials used to invert the laplace transform

Given the Laplace transform F(s) of a function f(t), we develop a new algorithm to find an approximation to f(t) by the use of the classical Jacobi polynomials. The main contribution of our work is the development of a new and very effective method to determine the coefficients in the finite series expansion that approximation f(t) in terms of Jacobi polynomials. Some numerical examples are illustrated.