非线性对流扩散问题的差分-流线扩散法

1．引言流线扩散法（简称SD方法）是由Huzhes和Brooks在1980年前后提出的一种数值求解对流占优扩散问题的新型有限元算法．随后，Johnson和N8vert将SD方法推广到发展型对流扩散问题（［1］，［2］，［3］）．熟知，对于对流扩散问题，标准有限元法虽具有高阶精度，但常产生数值振荡；古典人工粘性Galerkin法更具有较好的稳定性，但仅具有一阶精度．而（SD方法兼具良好的数值稳定性和高阶精度，因此得到了越来越多的重视，对于发展型对流扩散问题，传统的SD方法均采用时空有限元．这样做，虽然可使时间和空间方向上的精度很好的协调起…     

对流反应扩散方程的SUPG稳定化时空有限元解的误差估计（英文）

将时空有限元方法和流线扩散迎风Petrov-Galerkin方法(SUPG)相结合,构造对流扩散反应方程的一种全离散稳定化时空有限元方法.和传统的SUPG方法不同,本文为得到高精度尤其是时间高精度格式,在时空两个方向同时使用离散变分形式.该类格式曾被工程师用来数值模拟一些实际问题,但很难看到相关文献的理论分析证明.本文时间方向利用Gauss-Legendre和Gauss-Lobatto积分,并和有限元方法相结合,证明数值解的稳定性和误差估计.不但去掉时空网格的限制条件,而且将时间和空间变量解耦,克服了时空有限元方法在建立格式时由于时空变量统一处理而导致的理论分析和数值模拟中的高维度难度和复杂性,本文不需要引入对偶问题的证明思路丰富了稳定化SUPG时空有限元方法的理论.     

对流反应扩散方程的稳定化时间间断时空有限元解的误差估计

在流线迎风Petrov-Galerkin（SUPG）稳定化有限元数值格式的基础上,结合时间方向的变分离散,构造对流反应扩散方程的稳定化时间间断时空有限元格式.该类格式在工程上有一些数值模拟应用,但相关文献没有看到类似数值格式的理论证明.本文以Radau点为节点,构造时间方向的Lagrange插值多项式,证明了稳定化有限元解的稳定性,时间最大模、空间L²（Ω）-模误差估计.文中利用插值多项式和有限元方法相结合的技巧,解耦时空变量,去掉了时空网格的限制条件,提供了时间间断稳定化时空有限元方法的理论证明思路,克服了因时空变量统一导致的实际计算时的复杂性.     

带有对流项的拟线性Sobolev方程的差分-流线扩散法

1　引　　言流线扩散法 (Stream line- Diffusion method,简称 SD方法 )是由 Hughes和 Brooks在文献 [1]中提出 ,并由 Johnson等人 (文献 [2 ]- [4])发展起来的求解对流占优扩散问题 (包括双曲型问题 )的一种有效的数值方法 .SD方法兼具有良好的数值稳定性和高阶收敛精度已广泛地应用于计算流体等诸多问题 .然而 ,传统的 SD方法均采用时空有限元求解发展型问题 .这样 ,虽可使时间和空间方向上的精度很好的协调起来 ,却增大了实际计算的复杂程度 ;对非线性问题也不便进行线性化处理 .孙澈等人在文献 [5 ]中对对流扩散问题提出了仅对空间…     

非线性对流扩散问题的预测校正型FDSD格式

1 引言 流线扩散法(简称SD方法)是由Hughes和Brooks提出,并经Johnson等人发展的一种数值求解对流占优扩散问题的一种有效的数值方法。然而,传统的SD方法利用时-空有限元求解发展型问题,导致对高维问题工作量过于庞大,其编程实现较复杂,对非线性问题也不便进行线性化处理,为此,孙澈提出了仅对空间域作有限元离散,而对时间域作差分离散的差分-流线扩散法(以下简称FDSD方法),主要讨论了拟线性     

非定常线性化Navier-Stokes方程的非协调流线扩散有限元法分析

对非定常线性化Navier-Stokes方程提出了非协调流线扩散有限元方法．用向后Euler格式离散时间,用流线扩散法处理扩散项带来的非稳定性．速度采用不连续的分片线性逼近,压力采用分片常数逼近．得到了离散解的存在唯一性以及在一定范数意义下离散解的稳定性和误差估计．     

一阶双曲问题的间断流线扩散法

1．引言众所周知，求解一阶双曲问题的Galerkin有限元法，仅具有次最优LZ一收敛阶估计，难于建立H＼误差估计【‘1，且Gderkill有限元解常呈现伪数值振荡．为改善计算精度与稳定性，诸多非标准有限元解法相继提出，其中，间断（Discontinuous）Galerkin有限元法（以下简称DG方法）与流线扩散（StreamlineDiffusion）有限元法（以下简称SD法）是两种具有鲜明特点，较为成功的算法．具体地，DG方法是一种迎风型显式算法，它从入流边界开始，沿流场方向，自上游往下游，逐个单元进行解算，计算十分简便且可局部并行化．SD方法则是一种P…     

对流扩散问题的Crank-Nicolson差分-流线扩散法

1　引　言Streamline- Diffusion method (SD方法 )是近年来 Hughes和 Brooks提出的一种求解定常的对流占优和对流扩散问题的人工粘性有限元方法[1 ] ,[2 ] ,它具有标准有限元方法的高阶精度特点和人工粘性 Galerkin方法的稳定性特点 ,因此越来越受到人们的重视 .现在 ,SD方法已被推广到 Euler方程和 Navier- Stokes方程等发展型对流扩散问题[3 ] [4] ,但是常常采用时空有限元 [3 ] [5] ,这样能把时间和空间的精度很好地统一起来 ,却增大了数值计算的复杂性 ,基于此 [6 ]对非线性的对流占优扩散问题提出一种 Finite Difference- Strea…     

一个求解多维守恒律方程组的二阶显式有限元格式

１．引言 近年来,在非结构网格上求解双曲型守恒律的数值方法引起了较为广泛的关注,出现了有限体积方法［１］,间断 Ｇａｌｅｒｋｉｎ方法 ［２］,流线扩散方法［３］,以及 ＮＮＤ格式 ［４］等．我们在［６,７］中提出了一种求解双曲型守恒律方程式的有限元方法,它是在一个求解对流扩散问题的有限元方法 ［５］的基础上发展起来的．它是一个显式有限元方法,因此计算量很小．在这个方法中,我们将任意维的问题归结为在单元棱边上的一维计算,引入了积分因子,因此在单元内部可以容纳边界层．这样,它特别适合于对流占优问题以及双曲…     

对流扩散方程的间断时空有限元方法的误差估计

研究了一类线性对流扩散方程的间断时空有限元方法,即空间连续,时间允许间断的时空有限元方法.将有限元方法和有限差分方法相结合,在每一时间层上充分利用Lagrange插值多项式在Radau点处的特性,给出了有限元解的最优阶L∞(L2)模误差估计.     

Estimating a survival function with incomplete cause-of-death data

We propose a random censorship model which permits uncertainty in the cause of death assessments for a subset of the subjects in a survival experiment. A nonparametric maximum likelihood approach and a “self-consistency” approach are considered. The solution sets corresponding to both approaches are found. They are infinite and identical. Only some of the solutions are consistent; i.e., the MLEs and self-consistent estimators are not consistent in general. Two estimates are thus proposed and their asymptotic properties are studied. It is shown that both estimates are strongly consistent and converge to Gaussian processes. The covariance structures of these Gaussian processes are derived.     

Some properties of singular integral operators over an open curve Dedicated to the 85th birthday of Prof.Lu Jinake

In this paper, the stability properties, the endpoint behavior and the invertible relations of Cauchy-type singular integral operators over an open curve are discussed. If the endpoints of the curve are not special, this type of operators are proved to be stable. At the endpoints, either the singularity or smoothness of the operators are exactly described. And the function sets or spaces on which the operators are invertible as well as the corresponding inverted operators are given. Meanwhile, some applications for the solution of Cauchy-type singular integral equations are illustrated.     

Depth notions for orthogonal regression

Global depth, tangent depth and simplicial depths for classical and orthogonal regression are compared in examples, and properties that are useful for calculations are derived. The robustness of the maximum simplicial depth estimates is shown in examples. Algorithms for the calculation of depths for orthogonal regression are proposed, and tests for multiple regression are transferred to orthogonal regression. These tests are distribution free in the case of bivariate observations. For a particular test problem, the powers of tests that are based on simplicial depth and tangent depth are compared by simulations.     

Some properties of singular integral operators over an open curve Dedicated to the 85th birthday of Prof. Lu Jianke

In this paper, the stability properties, the endpoint behavior and the invertible relations of Cauchy-type singular integral operators over an open curve are discussed. If the endpoints of the curve are not special, this type of operators are proved to be stable. At the endpoints, either the singularity or smoothness of the operators are exactly described. And the function sets or spaces on which the operators are invertible as well as the corresponding inverted operators are given. Meanwhile, some applications for the solution of Cauchy-type singular integral equations are illustrated.     

具有双裂纹的弹性复合材料板承受剪切冲击时的动应力强度因子

本文研究了两个材半限弹性的接合面附近存在与接合面平行的双裂纹，并承受剪切冲击时的瞬态应力，运用付里叶（Ｆｏｕｒｉｅｒ）和拉普拉斯（Ｌａｐｌａｃｅ）变换，将问题归结为求解二元积分方程，求解时将裂纹所在面上，下的位移差展成级数，并让其自动满足裂纹面外的位移差为零的条件，利用裂纹面上的边界条件和施密特（Ｓｃｈｍｉｄｔ）方法求解级数中的待定系数，在拉普拉斯像空间中，求得动应力强度因子，并将其数值地逆变换至     

Pseudospectra and stability radii for analytic matrix functions with application to time-delay systems

Definitions for pseudospectra and stability radii of an analytic matrix function are given, where the structure of the function is exploited. Various perturbation measures are considered and computationally tractable formulae are derived. The results are applied to a class of retarded delay differential equations. Special properties of the pseudospectra of such equations are determined and illustrated.     

Some properties of complex matrix-variate generalized Dirichlet integrals

Dirichlet integrals and the associated Dirichlet statistical densities are widely used in various areas. Generalizations of Dirichlet integrals and Dirichlet models to matrix-variate cases, when the matrices are real symmetric positive definite or hermitian positive definite, are available [4]. Real scalar variables case of the Dirichlet models are generalized in various directions. One such generalization of the type-2 or inverted Dirichlet is looked into in this article. Matrix-variate analogue, when the matrices are hermitian positive definite, are worked out along with some properties which are mathematically and statistically interesting.     

Forces of rails for electromagnetic railguns

In this paper, using electromagnetic theory, the equations for the total magnetic force on the rails are deduced. Besides this, the equations for the changes of the magnetic force along with time and the running position of the armature under jointed pulse operating current are presented. Then, the equations for changes of the bending stress and shear stress in the rail along with time and the running position of the armature are given. Changes of the magnetic force distribution between the two rails along with the running position of the armature and other parameters are investigated. The total electromagnetic forces on the rail under jointed pulse operating current are analyzed. Distribution and changes of the bending stresses in the rail are studied. A number of results are obtained. The results are useful for design and application of the railgun system.     

直觉模糊关系的截集性质

定义了直觉模糊关系的截集以及并给出了它们的基本性质,同时分别讨论了自反、对称、传递直觉模糊关系与经典二元关系之间的等价刻画;其次,提出直觉模糊关系的定义域与值域的概念;最后,分析了直觉模糊关系合成的截集性质.     

凹角型区域椭圆边值问题的自然边界归化

In this paper, the natural boundary reduction for some elliptic boundary value problems with concave angle domains and their natural boundary methods are investigated. The natural integral equations and the Poisson integral formulae are given. The finite element methods of the natural integral equations are discussed in details. The convergences of the approximate solutions and their error estimates are obtained. Finally, some numerical examples are presented to show that our methods are effective.