A REMAPPING METHOD BASED ON MULTI-POINT FLUX CORNER TRANSPORT UPWIND ADVECTION ALGORITHM

A local remapping algorithm for scalar function on quadrilateral meshes is described. The remapper from a distorted grid to a rezoned grid is usually regarded as a conservative interpolation problem. The present paper introduces a pseudo time to transform the interpolation into an initial value problem on a moving grid, and construct a moving mesh method to solve it. The new feature of the algorithm is the introduction of multi- point information on each edge, which leads to the numerical flux consistent with grid node motion. During the procedure of deriving scheme, we illustrate a framework about how the algorithms on a rectangular mesh are easily generated to those on a moving mesh. The basic ideas include： （i） introducing coordinate transformation, which maps the irregular domain in physical space to a perfectly regular computational domain, and （ii） deriving finite volume methods in the physical domain, which can be viewed as a discretization of the transformed equation. The resulting scheme is second-order accurate, conservative and monotonicity preserving. Numerical examples are carried out to show the good performance of ore＂ schemes.     

不可压缩流动的并行数值方法

不可压缩流动的数值模拟是计算流体力学的重要组成部分. 基于有限元离散方法, 本文设计了不可压缩Navier-Stokes (N-S)方程支配流的若干并行数值算法. 这些并行算法可归为两大类: 一类是基于两重网格离散方法, 首先在粗网格上求解非线性的N-S方程, 然后在细网格的子区域上并行求解线性化的残差方程, 以校正粗网格的解; 另一类是基于新型完全重叠型区域分解技巧, 每台处理器用一局部加密的全局多尺度网格计算所负责子区域的局部有限元解. 这些并行算法实现简单, 通信需求少, 具有良好的并行性能, 能获得与标准有限元方法相同收敛阶的有限元解. 理论分析和数值试验验证了并行算法的高效性     

动态区间三角模糊多属性决策的TOPSIS扩展方法

针对各决策时段的时间权重已知,属性值以区间三角模糊数形式给出的动态多属性决策问题,提出了一种基于逼近于理想解排序(TOPSIS)拓展的决策分析方法.方法首先利用给出的动态区间三角模糊加权平均(DITFWA)算子对各时段的评价值进行集成,以获取综合评价值.然后依据传统TOPSIS法的基本思想,对整个方案集进行排序并择优.最后给出一个实例进行分析,所得结果表明了该方法的实用性和可行性.     

余拟三角双单子

给出了余卷积、余中心元、余扭元、余拟三角双单子的定义,并在单子T的线性型和T-模范畴的辫子之间及单子T的余扭元和T-模范畴的扭元之间建立了双射.     

分类讨论的数学思想及其应用（4）

第四讲：分类讨论的运用（一）从前面三讲中我们已经知道,解分类讨论题的主要过程是进行逻辑划分和对每一类做出讨论、证明、求解等等．高考不仅是数学知识的考查,也是数学思想方法的考查．高考的“能力立意”,主要是通过在数学思想的指导下,如何运用数学方法解决问题来体现的．     

UNIFORM SUPERCONVERGENCE OF A FINITE ELEMENT METHOD WITH EDGE STABILIZATION FOR CONVECTION-DIFFUSION PROBLEMS

In the present paper the edge stabilization technique is applied to a convection-diffusion problem with exponential boundary layers on the unit square, using a Shishkin mesh with bilinear finite elements in the layer regions and linear elements on the coarse part of the mesh. An error bound is proved for ‖πu-u^h‖Е, where πu is some interpolant of the solution u and uh the discrete solution. This supercloseness result implies an optimal error estimate with respect to the L2 norm and opens the door to the application of postprocessing for improving the discrete solution.     

BLOCK-TRIANGULAR PRECONDITIONERS FOR SYSTEMS ARISING FROM EDGE-PRESERVING IMAGE RESTORATION

Signal and image restoration problems are often solved by minimizing a cost function consisting of an l2 data-fidelity term and a regularization term. We consider a class of convex and edge-preserving regularization functions. In specific, half-quadratic regularization as a fixed-point iteration method is usually employed to solve this problem. The main aim of this paper is to solve the above-described signal and image restoration problems with the half-quadratic regularization technique by making use of the Newton method. At each iteration of the Newton method, the Newton equation is a structured system of linear equations of a symmetric positive definite coefficient matrix, and may be efficiently solved by the preconditioned conjugate gradient method accelerated with the modified block SSOR preconditioner. Our experimental results show that the modified block-SSOR preconditioned conjugate gradient method is feasible and effective for further improving the numerical performance of the half-quadratic regularization approach.     

Multi-mesh adaptive finite element algorithms for constrained optimal control problems governed by semi-linear parabolic equations

In this paper, we derive a posteriori error estimators for the constrained optimal control problems governed by semi-linear parabolic equations under some assumptions. Then we use them to construct reliable and efficient multi-mesh adaptive finite element algorithms for the optimal control problems. Some numerical experiments are presented to illustrate the theoretical results.     

带有临界点的解析函数的圆模式逼近

一个圆模式是指复平面C上具有特定交角的一种圆格局.给定有界单连通区域ΩC内一个具有有限多个临界点的解析函数F,首先利用有分枝圆模式枝术构造了F的离散近似解,然后证明了这个近似解序列在Ω的紧子集上一致收敛于该解析函数F.这为带有临界点的解析函数的数值计算提供一种新的方法.     

概率求解的类型

<正>开动脑筋求概率,最为关键的有两点,第一是要清楚我们所关注的事件包含了哪些结果;第二是要清楚所有机会均等的结果.这两种结果的个数之比就是我们所要求的概率.因此,在计算概率的时候,我们所关注的结果和所有机会均等的结果这两个方面的找寻变得尤为重要.一、寻找我们所关注的结果在大多数情况下,所有机会均等的结果比较好找,对于我们所关注的结果,我们可以通过列举的方法寻找.图1例1(2012年内江)如图1所示,A、B是边长为1的正方形组成的网格的两个格点,在格点中任意放置点C,恰好能使△ABC的面积为1的概率是.