蒸汽沉淀化学反应方程混合元法的离散格式研究

蒸汽沉淀化学反应过程有着极其广泛的应用,其数学模型归结为一个包含流速场,温度场,压力场和气体溶质场的非线性偏微分方程组．用混合有限元方法研究蒸汽沉淀化学反应方程组,导出其半离散化和全离散化的混合元格式,并证明这些格式的解的存在性和收敛性(误差估计)．用混合元法处理究蒸汽沉淀化学反应方程组,可以同时求出流速场,温度场,压力场和气体溶质场的数值解. 因此该研究既具有重要的理论意义,又具有广泛的应用前景．     

非定常的热传导-对流问题的非线性Galerkin混合元法(Ⅱ):向后一步的Euler全离散化格式

In this paper, a fully discrete format of nonlinear Galerkin mixed element method with backward one-step Euler discretization of time for the non stationary conduction-convection problems is presented. The scheme is based on two finite element spaces XH and Xh for the approximation of the velocity, defined respectively on a coarse grid with grids size H and another fine grid with grid size h<< H, a finite element space Mh for the approximation of the pressure and two finite element spaces AH and Wh, for the approximation of the temperature,also defined respectivply on the coarse grid with grid size H and another fine grid with grid size h. The existence and the convergence of the fully discrete mixed element solution are shown. The scheme consists in using standard backward one step Euler-Galerkin fully discrete format at first L0 steps (L0 2) on fine grid with grid size h, but using nonlinear Galerkin mixed element method of backward one step Euler-Galerkin fully discrete format through L0 + 1 step to end step. We have proved that the fully discrete nonlinear Galerkin mixed element procedure with respect to the coarse grid spaces with grid size H holds superconvergence.     

关于对流方程的离散化问题

本讨论了用矩形同格离散化肘流方程的一般方法,若格式含有N个同点,则其最高阶格式为N-2阶。同时构造了一些新的高精度差分格式．     

离散格式稳定的充分条件的改进

本文改进了A.A.萨多尔斯劳[1]中判稳的充分条件,把条件B≥εE+0.5τA,B≥εE放宽为:基本上只要求B>0.5τA,B>0.     

抛物型初边值问题的有限元与边界积分耦合的离散化及其误差分析

1．引言边界元方法是近二十几年来迅速发展起来的一类新的偏微分方程的数值方法．它的独特之处是将空间的维数降低一维,从而倍受工程技术人员的青睐,并在工程技术与计算数学领域得到越来越广泛的重视和研究．对椭圆型问题,边界元方法的理论与应用研究已取得丰硕成果;对发展型问题,近年来在理论方面的研究也已取得重要进展［6－11］．但边界元方法难以处理非均质问题,而有限元对各类问题及各种区域具有较好的适应性,将两者结合起来可充分发挥各自的优点．文山提出了一种抛物方程初边值问题的有限元与边界积分的耦合方法,其主要思想是…     

非定常的热传导-对流问题的非线性Galerkin混合元法(Ⅱ):向后一步的Euler全离散化格式

1．引言本文的工作主要是讨论非定常的热传导一对流问题的向后一步的Euler全离散化的非线性Galerkin混合元解的存在性及其误差估计．该工作是对山中的同一问题研究的第二部分．在第一部分［1］，我们已经讨论了此问题的半离散化的情形．由于所研究的目标都是非定常的热传导一对流问题，其背景是相同的，在此将不重复了，请参考［1］．本文的安排如下，52先回顾非定常的热传导一对流问题的混合元解的经典性质．53回顾半离散化的非线性Galerkin混合元解的性质，并导出后续讨论需要的一些关于时间导数的估计．54讨论向后一步的Euler全离散化…     

非饱和土壤水流问题的CN有限元格式

首先给出二维非饱和土壤水流问题基于Crank-Nicolson(CN)方法的具有时间二阶精度的半离散化格式,然后直接从CN时间半离散化格式出发,建立具有时间二阶精度的全离散化CN有限元格式,并给出误差估计,最后用数值例子说明全离散化CN有限元格式的优越性.这种方法可以绕开关于空间变量的半离散化格式的讨论,提高时间离散的精度,极大地减少时间方向的迭代步,从而减少实际计算中截断误差的积累,提高计算精度和计算效率.     

算子方程离散格式判稳的充分条件

萨马斯基曾给出判稳的充分条件,但它涉及估计算子的模或特征值,这在一般情况下是困难的,不容易检验.本文给出一种易于检验的充分条件,即把稳定性与一代数方程组的Jacobi迭代法的迭代阵的最大特征值联系起来,从而可利用迭代法收敛的某些已知结果来判别稳定性,其中特别方便的是利用矩阵的对角占优条件.本方法的特点是适用于一般的非均匀有限元剖分.     

空气污染方程的全离散化混合元格式

本文研究空气污染方程,导出其全离散化的混合元格式,证明该格式的全离散化混合元解的存在性和收敛性(误差估计).     

非饱和土壤水流方程的CN广义差分法

首先给出二维非饱和土壤水流方程时间二阶精度的Crank-Nicolson(CN)时间半离散化格式,然后直接从CN时间半离散化格式出发,建立具有时间二阶精度的全离散化CN广义差分格式,并给出误差分析,最后用数值例子验证全离散化CN广义差分格式的优越性.这种方法能提高时间离散的精度,极大地减少时间方向的迭代步,从而减少实际计算中截断误差的积累,提高计算精度和计算效率.而且该方法可以绕开对空间变量的半离散化广义差分格式的讨论,使得理论研究更简便.     

A hybrid method for inverse cavity scattering problem for shape

In this paper, we give a hybrid method to numerically solve the inverse open cavity scattering problem for cavity shape, given the scattered solution on the opening of the cavity. This method is a hybrid between an iterative method and an integral equations method for solving the Cauchy problem. The idea of this hybrid method is simple, the operation is easy, and the computation cost is small. Numerical experiments show the feasibility of this method, even for cases with noise.     

一种求解非线性互补问题的方法及其收敛性

本文将Newton方法和外梯度方法相结合,提出了一种求解非线性互补问题的方法,证明了此方法的全局收敛性和超线性收敛性,在适当的条件下给出了一个有限终止结果。数值实验表明,此方法是有效的。     

乘子方法中的参数选择

Di Pillo和Grippo提出的含参数C〉0的增广Lagrangian函数中，使用了最大函数，该函数可能在无穷多个点处不可微．为了克服这个问题，濮定国在2004年提出了一类带新的NCP函数的乘子法．该方法在增广Lagrangian函数和原问题之间存在很好的等价性；同时该方法具有全局收敛性，且在适当假设下，具有超线性收敛率．但是在该方法中，要求参数C充分大．为了实现算法及提高算法效率，本文给出了一个有效选择参数C的方法．     

变步长非单调模式搜索法

A varied steplength nonmonotone pattern search method is proposed in this paper. The varied steplength search strategy is designed in this method such that the pattern direction is more approximated to efficient descent direction. The interpolation and nonmonotone technique are used for improving local search and global convergence. The theoretical and numerical results show that this method is an efficient direct search method.     

多源验前信息下先验分布的稳健融合方法

根据多种先验分布与似然函数尾部特性的比较,给出了多源验前信息下先验分布的稳健融合方法.讨论了由该方法得到的融合先验分布的后验稳健性问题.最后的数值例子表明,由该方法得到的融合先验分布具有较好的稳健性,进一步验证了该方法的有效性.     

无记忆非拟 Newton 算法的导出和全局收敛性

In this paper, a new class of memoryless non-quasi-Newton method for solving unconstrained optimization problems is proposed, and the global convergence of this method with inexact line search is proved. Furthermore, we propose a hybrid method that mixes both the memoryless non-quasi-Newton method and the memoryless Perry-Shanno quasi-Newton method. The global convergence of this hybrid memoryless method is proved under mild assumptions. The initial results show that these new methods are efficient for the given test problems. Especially the memoryless non-quasi-Newton method requires little storage and computation, so it is able to efficiently solve large scale optimization problems.     

有限元法中大单元的构造

在通常的有限元法中,单元内的插值多项式的阶数固定不变,通过加密剖分网格来提高精度.大单元法则剖分的网格固定不变而通过增加单元内逼近级数的项数来提高精度. 本文提出采用两套变量的办法来构造大单元,即单元内采用一套变量,单元的边界上采用另一套变量,然后用杂交罚函数法把两者联系起来.这种方法能适用于任何椭圆型方程,任意几何形状区域以及任何复杂的边界条件.本文用严密的数学方法证明了:在一般情况下,这种方法的精度比通常的有限元法和文[7]的大单元法高得多.即在达到相同的精度时,本文方法所需要的自由度(即未知数数目)比上述两种方法少得多.     

Decoupled modified characteristics finite element method for the time dependent Navier–Stokes/Darcy problem

In this paper, a modified characteristics finite element method for the time dependent Navier–Stokes/Darcy problem with the Beavers–Joseph–Saffman interface condition is presented. In this method, the Navier–Stokes/Darcy equation is decoupled into two equations, one is the Navier–Stokes equation, the other is the Darcy equation, and the Navier–Stokes equation is solved by the modified characteristics finite element method. The theory analysis shows that this method has a good convergence property. In order to show the effect of our method, some numerical results was presented. The numerical results show that this method is highly efficient. Copyright © 2013 John Wiley & Sons, Ltd.     

The Homotopy Perturbation Renormalization Group Method to Solve the WKB Problem with Turn Points

In this paper, we give the homotopy perturbation renormalization group method, this is a new method for turning point problem. Using this method, the independent variables are introduced by transformation without introducing new related variables and no matching is needed. The WKB approximation method problem can be solved.     

A smoothing QP-free infeasible method for nonlinear inequality constrained optimization

In this paper,a smoothing QP-free infeasible method is proposed for nonlinear inequality constrained optimization problems.This iterative method is based on the solution of nonlinear equations which is obtained by the multipliers and the smoothing Fisher-Burmeister function for the KKT first-order optimality conditions.Comparing with other QP-free methods, this method does not request the strict feasibility of iteration.In particular,this method is implementable and globally convergent without assuming the strict complementarity condition and the isolatedness of accumulation points.Furthermore,the gradients of active constraints are not requested to be linearly independent.Preliminary numerical results indicate that this smoothing QP-free infeasible method is quite promising.