求解二次Lagrangian有限元方程的代数两水平方法

基于矩阵图集的粗化算法,构造一种新的插值算子,提出了瀑布型代数两重网格法;然后结合部分几何信息,提出了求解二次Lagrangian有限元方程的代数两水平方法.数值实验表明该算法稳健性强、计算量更少.     

求解三维高次拉格朗日有限元方程的代数多重网格法

本文针对带有间断系数的三维椭圆问题,讨论任意四面体剖分下的二次拉格朗日有限元方程的代数多重网格法．通过分析线性和高次有限元空间之间的关系,我们给出了一种新的网格粗化算法和构造提升算子的代数途径．进一步,我们还对新的代数多重网格法给出了收敛性分析．数值实验表明这种代数多重网格法对求解二次拉格朗日有限元方程是健壮和有效的。     

新外推完全多重网格法北大核心

使用新外推公式和高阶插值算子,为相邻细层提供好的初值,对初值使用磨光算子磨光几次后,再调用V型多重网格法求得该层数值解,构造了基于四阶紧致差分格式的新外推完全多重网格法.数值实验表明,与对比算法相比,新算法迭代次数少、计算时间短、稳健性强.     

新外推完全多重网格法

使用新外推公式和高阶插值算子,为相邻细层提供好的初值,对初值使用磨光算子磨光几次后,再调用V型多重网格法求得该层数值解,构造了基于四阶紧致差分格式的新外推完全多重网格法.数值实验表明,与对比算法相比,新算法迭代次数少、计算时间短、稳健性强.     

等几何分析的多重网格共轭梯度法

提高NURBS基函数阶数可以提高等几何分析的精度,同时也会降低多重网格迭代收敛速度.将共轭梯度法与多重网格方法相结合,提出了一种提高收敛速度的方法,该方法用共轭梯度法作为基础迭代算法,用多重网格进行预处理.对Poisson(泊松)方程分别用多重网格方法和多重网格共轭梯度法进行了求解,计算结果表明:等几何分析中采用高阶NURBS基函数处理三维问题时,多重网格共轭梯度法比多重网格法的收敛速度更快.     

解Stokes方程的一种无散稳定二次有限体积法格式

在三角形网格上构造了一种求解Stokes方程的Lagrange二次有限体积法格式.取连续的二次有限元空间与间断的线性有限元空间分别作为Stokes方程的速度项与压力项的试探空间,从而保证了离散方程的速度解在宏元三角形单元上满足局部质量守恒性,且有限元空间对自然满足所谓的inf-sup条件.采用特殊的有限体积法映射与对偶剖分,求解Stokes方程的Lagrange二次有限体积法格式等价于相对应的有限元法格式,因此确保了有限体积法格式的无条件(无需约束三角形网格的几何形状)稳定性和关于速度项的最优阶H1范数的误差估计.最后,数值实验展示了理论结果的正确性以及有限体积法的数值模拟在计算流体力学中的有效性.     

耦合Navier-Stokes/Darcy模型多重网格方法的有限元实现(英文)

本文研究耦合Navier-Stokes/Darcy模型问题.构造一种从粗网格到细网格的有限元空间插值方法,不但简化了数值积分的单元匹配,也保证了数值积分的精度.利用基于有限元空间的多重网格方法,获得与直接法求解耦合问题误差相同的收敛阶,推广两重网格方法的结果.     

非协调Wilson有限元的多重网格方法

§1.引言 非协调Wilson有限元[1—3]对解弹性力学方程有实用价值,在工程上有用。本文分析Wilson元的多重网格法,给出用多重网格方法求得的近似解按L~2模和能量模的最佳收敛阶误差估计。对于W-循环,可以证明其计算量与离散空间的维数为同一量级O(N_k)。 考虑二阶椭圆Dirchlet边值问题:     

经济的瀑布型多重网格法(ECMG)

提出一种新的经济的瀑布型多重网格法(ECMG), 和通常的瀑布型多重网格法(CMG)的工作量相比, 新的瀑布型多重网格法在每层上的工作量 都相应的减少, 尤其是粗网格上的工作量将大量的减少. 新格式的误差和通常的 瀑布型多重网格法一样, 都具有最优精度. 最后给出数值算例 来验证所得理论的结果.     

带插值的自适应网格重构算法求解带移动热源的反应扩散方程的理论分析

本文研究一个带插值的网格重构算法求解一类带移动热源的反应扩散方程. 算法包括两步: 第一步是用旧时间网层上的计算解计算新时间层上的空间网格; 第二步是使用有限差分方法在新时间层 空间网格上离散方程, 并且将旧时间层上计算解的插值作为初始值. 对于时间, 我们获得了一阶收敛结果. 对于空间, 我们证明了使用线性插值算法的一阶收敛性和使用二次插值算法的二阶收敛性. 数值例子肯定了本文的理论结果.     

Qualitative Analysis of Bifurcating Solutions in the Lengyel-Epstein Model

One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the＇living world. In his seminal paper ＂The Chemical Basis of Morphogenesis＂, Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates（1990） on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing＇s prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows     

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.     

(0,1 ;0)-INTERPOLATION ON INFINITE INTERVAL (-∞, +∞)

In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H′n(x) and the first derivatives at the zeros of H′n(x).     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

Journal of the Operations Research Society of China Special issue on Operations Research in Healthcare Management

正Guest Editors:Hong Chen,Shanghai Jiao Tong University,Shanghai,China Guohua Wan,Shanghai Jiao Tong University,Shanghai,China David Yao,Columbia University,New York,USA Scope:Healthcare delivery worldwide has been fraught with high cost,low efficiency and poor quality of patient care service.For the field of operations research(OR),healthcare offers some of the biggest challenges as well as best opportunities in     

ANALYSIS IN THEORY AND APPLICATIONS Vol. 30, 2014 CONTENTS

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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.     

An alternative mathematical algorithm for the photo- and videokeratoscope

Due to the resolution of current laser technology, the accuracy of corneal topography as measured by the videokeratoscope is no longer adequate to provide precise enough data for refractive surgery or for the fitting of customized contact lenses. We present an algorithm for recovering corneal topography that makes use of modern differential geometric techniques and numerical descent in Sobolev spaces. We believe this algorithm may be used with the photo- and videokeratoscope to increase the accuracy of the recovered corneal topography.