空间网格上的三次GC^1插值格式

本文得到了由三次参数多项式构造的ＧＣ＾１插值格式，该插值格式定义在由空间三角一菜和空间四边形构成的空间网格上，并通过该网格的所有网点，同时在每个网点处以事先给定的平面为切平面。     

一个定义在任意三角网格上的五次GC′插值格式

A kind of GC′ surface constructing scheme on arbitrary triangular mesh is presented. The surface formed by this scheme can pass the given position vectors and take the given planes as its tangent planes at the vertices of the triangular mesh. Triangular mesh referred here is a set of space triangles and their faces such that the intersection of any two edges in this set is a vertex or an empty set.     

复三次样条插值

一、设K是复平面上的光滑闭曲线,在其上按逆时针方向取分划K_j表示K上从t_(j-1)到t_j的弧段,s_j表示从t_1到t_j的弧长。记h_j=t_j-t_(j-1)、△=max|h_j|、△=min|h_j|、△=max(s_j-s_(j-1))。 设f(t)∈C(K),q△(t)是f(t)关于分划△的复三次插值样条,即q△(t)满足:     

三次样条插值的收敛性

设f(x)∈C_[a,b],△_n是区间[a,b]的分划 △_n:a=x_0相似文献   

三次样条的Hermite-Birkboff插值

设Δ:0=x_0相似文献   

长方体网格上的三元连分式的插值

本文利用递推公式构造了一个空间长方体网格上的三元连分式的插值公式,插值的存在性和唯一性得到了证明,一个数例说明了插值方法的有效性。     

无限多个基点上的三次样条函数插值

Schoenberg曾提出如下的问题: 给定一个严格增加的序列Δ=(x_i)_(-∞)~∞及相应的有界双无限序列(y_i)_(-∞)~∞,是否存在一个有界的三次样条函数s,它以Δ为基点且对所有i,有     

Besov 空间上的算子插值定理

本文研究了算子的插值问题.利用Riesz-Thorin定理的证明方法,并运用Daubechies小波得到了Besov空间上的线性算子的插值定理.     

一个三次样条插值定理

C.Davis和W.J.Kammerer曾先后用不同的方法证明了如下定理: 设y_0,y_1,…,y_n为实数,满足y_0>y_1,y_1y_3,…,则存在唯一的一个n次多项式P_n(x)和一组点x_0,x_1,…,x_n使得P_n(x_i)=y_i(i=0,1,…,n),P′_n(x_i)=0(i=1,2,…,n-1),0=x_0相似文献   

多边形网格上扩散方程新的单调格式

 本文在星形多边形网格上, 构造了扩散方程新的单调有限体积格式.该格式与现有的基于非线性两点流的单调格式的主要区别是, 在网格边的法向流离散模板中包含当前边上的点, 在推导离散法向流的表达式时采用了定义于当前边上的辅助未知量, 这样既可适应网格几何大变形, 同时又兼顾了当前网格边上物理量的变化. 在光滑解情形证明了离散法向流的相容性.对于具有强各向异性、非均匀张量扩散系数的扩散方程, 证明了新格式是单调的, 即格式可以保持解析解的正性. 数值结果表明在扭曲网格上, 所构造的格式是局部守恒和保正的, 对光滑解有高于一阶的精度, 并且, 针对非平衡辐射限流扩散问题, 数值结果验证了新格式在计算效率和守恒精度上优于九点格式.     

保凸C^1分段二次多项式插值方法

本导出了二次多项式保凸的充要条件,通过插值部分新节点,得到了一种新的保凸Ｃ＾１分段二镒多项式插值函数。     

A Superconvergence Analysis for Finite Element Solution by the Interpolant Postprocessing on Irregular Meshes for Smooth Problem

The post-processing procedure is given by an interpolant postprocessing of the finite element solution by appropriately-defined finite dimensional subspaces. The corresponding superconvergence is established on general quasi-regular finite element partitions.     

在拼接点达到GC2连续的双二次曲线与样条的构造

本文研究了连续的双二次曲线,给出双二次曲线样条的构造方法.本方法适用在一些特定点上给定相对曲率并要求整个样条曲线GC2连续的一类问题,采用双二次曲线样条得到的样条曲线具有较好保凸性能.     

Hybrid Surface Mesh Adaptation for Climate Modeling

Solution-driven mesh adaptation is becoming quite popular for spatial error control in the numerical simulation of complex computational physics applications, such as climate modeling. Typically, spatial adaptation is achieved by element subdivision （h adaptation） with a primary goal of resolving the local length scales of interest. A sec- ond, less-popular method of spatial adaptivity is called ＂mesh motion＂ （r adaptation）; the smooth repositioning of mesh node points aimed at resizing existing elements to capture the local length scales. This paper proposes an adaptation method based on a combination of both element subdivision and node point repositioning （rh adaptation）. By combining these two methods using the notion of a mobility function, the proposed approach seeks to increase the flexibility and extensibility of mesh motion algorithms while providing a somewhat smoother transition between refined regions than is pro- duced by element subdivision alone. Further, in an attempt to support the requirements of a very general class of climate simulation applications, the proposed method is designed to accommodate unstructured, polygonal mesh topologies in addition to the most popular mesh types.     

b~(2)空间及b~(2)空间上的等距映射

等距映射在空间结构的研究中起着很重要的作用,是泛函分析研究的有利工具.本文将介绍一类特殊的F空间,b~(2)空间,然后给出该空间单位球面间满等距映射的表现定理,进而得出b~(2)空间单位球面上满等距映射的线性延拓结论.     

bp(2)空间中的等距映射

度量与线性性质是赋范空间的重要性质,因此,研究线性算子与等距算子的关系成为了泛函分析领域重要的研究课题.本文首先研究一类特殊的赋准范空间,即bp(2)空间的重要性质.然后给出bp(2)空间单位球面间满等距映射的表示定理及延拓性质.     

A note on the geometry of M 3 and symplectic structures on S 1 × M 3

We investigate the relationship between the geometry of a closed, oriented 3-manifold M and the symplectic structures on S ¹ × M. In most cases the existence of a symplectic structure on S ¹ × M and Thurstonșs geometrization conjecture imply the existence of a geometric structure on M. This observation together with the existence of geometric structures on most 3-manifolds which fiber over the circle suggests a different approach to the problem of finding a fibration of a 3-manifold over the circle in case its product with the circle admits a symplectic structure. This work was supported in part by a GEBIP grant from the Turkish Academy of Sciences and a CAREER grant from the Scientific and Technological Research Council of Turkey.     

具有重结点的B-样条曲面G1的连续条件

本文得到了关于两个双三次内部重结点B-样条曲面片G¹连续的充分必要条件和在公共边界线上控制向量的本征条件.这些条件直接由两个B-样条曲面的控制向量表示.文[10]证明了使用内部单结点的双三次B-样条曲面来构造G¹光滑曲面,局部格式不存在.使用本文的这些条件就可以构造出具有局部各式的G¹光滑造型.     

A Theory of Orbit Braids*

In this paper, the authors systematically discuss orbit braids in M × I with regards to orbit configuration space FG(M, n), where M is a connected topological manifold of dimension at least 2 with an effective action of a finite group G. These orbit braids form a group, named orbit braid group, which enriches the theory of ordinary braids.The authors analyze the substantial relations among various braid groups associated to those configuration spaces FG(M, n), F(M/G, n) and F(M, n). They also co...     

基于当地笛卡尔架构的无网格方法

提出了一种新的无网格方法,该方法是自动地在每一样点建立一个局部笛卡尔架构并选取相应的邻近点,然后运用全导数公式构造该样点的所有导数,它不需要任何网格单元,所以是彻底的无网格方法．数值算例表明,该方法具有很高的精度．