从一维母小波反投影二维母小波

提出了从一维母小波函数出发,反投影构造二维母小波函数,从而为二维母小波函数的构造开辟了另一条途径。     

图像边缘检测二维小波算法研究与实现

边沿作为图像视觉的最主要特征，成为图像信息获取的重要内容。小波变换具有检测局域突变的能力，而且可以结合多尺度信息进行检测，因此成为图像信息边缘检测的优良工具。根据二维小波变换的特点,分析了利用二维小波进行图像边缘检测的基本原理，并设计了利用二维小波变换进行多尺度边缘匹配的检测算法。基于研究结果，编写了计算机应用程序，进行实例分析。     

二维母小波函数的投影

由二维母小波函数的函数投影,得到二维母小函数与一维母小波函数的非张量积关系,指出当二维上波函数满足一定的条件时,其投影为一维线小波函数,二维小波变换可由春投影的一维小波变换实现。     

二维半线性抛物方程的二重网格差分算法

针对二维半线性抛物方程,本文提出了两种二重网格差分算法,并给出了误差估计。该算法能够在粗网格和细网格上线性地求解半线性问题。若重复算法的最后几步可以按粗网格步长任意阶地逼近细网格上的非线性解。     

不可分对称正交小波紧框架的构造

与可分小波相比,不可分小波更能捕捉高维信号的高频信息,正交框架在处理高维信号时能避免预滤波.为了更有效地处理高维信号,本文研究了不可分正交小波紧框架的构造,提出了一种由一维小波紧框架来构造高维不可分正交小波紧框架的方法,即先用张量积的方法构造高维小波紧框架,然后乘上一个具有一定性质的三角多项式.如果一维小波紧框架是对称的,用本文提出的方法构造的高维不可分的正交小波紧框架也是对称的.最后给出了一个构造算例.     

二维变系数抛物型方程高精度恒稳定的改进的Douglas格式

本文将算子方法和粘结系数方法相结合,构造出了求二维变系数抛物型方程的改进的Douglas格式,格式的截断误差阶达O(τ2+h4),并用Fourier分析方法讨论了格式的绝对稳定性.文末给出的数值例子表明了本文理论分析的正确性和所构造格式的有效性及优越性.长期以来,现有关于抛物型方程的差分格式都是对常系数方程而言的,本文较简便的给出了二维情形下变系数抛物型方程的差分解法,此方法完全可以推广到高维情形.     

基于DB小波无网格法:二维弹塑性问题

该文研究了基于Daubechies(DB)小波无网格方法对弹塑性问题中的分析。利用DB小波尺度函数作为基函数近似未知的场函数,不必类似有限元法和传统的无网格法花很大代价去构造所谓的形函数。该文利用新方法建立了增量格式的二维弹塑性问题的求解方案。二维弹塑性问题的数值算例证明了该方法的稳定性和有效性。     

结构物理参数的分频段加权辨识

利用小波分析多分辨率分析原理,建立线性系统多尺度动力平衡方程。将外荷载和线性系统在荷载作用下的响应作正交小波变换,得到各频段的小波系数,由多尺度动力平衡方程建立系统的参数识别方程。在不同频段根据系统的信噪比大小确定不同的加权值,对结构物理参数进行加权最小二乘辨识。该方法能较大地提高结构物理参数的识别精度,并且识别精度随着小波分解层次的增加而增大。     

无网格-精细积分算法在二维结构振动问题中的应用研究

将无网格-精细积分法用于二维结构振动问题的求解,通过瞬时最小势能原理构造与弹性动力学方程等效的能量泛函。由伽辽金无网格法在空间域内进行离散;在时间域上通过与Romberg积分相结合的精细积分法求解,得到了二维结构的固有频率和振型以及在不同激励作用下的位移、应力和速度响应。     

一类紧支撑对称双正交小波(英文)

摘要:研究伸缩因子为3紧支撑对称双正交小波的构造问题.任给一个插值对称的加细函数,本文提供 一个构造其对偶尺度函数的迭代算法,其对偶尺度函数的正则性可以达到任意水平,讨论了它的一些性 质,如对称性和衰减性.最后,给出构造算例.     

正交四重小波的收敛性与光滑性

1996年，Chui C K,与Lian JA 在不考虑其收敛性与光滑性的情况下，首次得出正交的二重小波，引起相当多人的注意，Jia R Q,Zhou DX等讨论三重小波的收敛性与光滑性，给出特例，指出Chui 与Lian的二重小波特例的收敛性与光滑性，洪东等讨论了四重小波的特例，本文在此基础上进一步讨论了正交四重小波的敛性与光滑性，给出兼有正交对称（反对称）的特例。     

双正交多小波的平衡及构造

将平衡概念引入到双正交多小波,给出相应的平衡条件,并证明了有关双正交多小波平衡的若干等价命题。最后给出了相应的构造方法及算例。     

2重正交多尺度函数和多小波的构造

基于正交单尺度函数,给出一种构造2重正交多尺度函数的方法。也给出对应正交多小波的显式构造公式。由于构造的2重正交多尺度函数中的个是所给的正交单尺度函数,另一个是新构造出的函数,因此这种多小波比相关的单小波具有更好的频率局部性。     

a尺度多重双正交小波包

小波包的引入使频域带的划分更加精细,更利于观察高频现象.本文在a(a2,a∈Z)尺度多重双正交小波基的基础上构造了a尺度双正交小波包.它在应用上灵活性很强.按此法可构造多种不同的双正交小波包.如同讨论2尺度双正交小波包一样,着重研究了a尺度双正交小波包的双正交性质并给出了相应的分解关系.     

A multiwavelet Galerkin method for Stokes problems using boundary integral equations

A multiwavelet Galerkin method for the simulation of two-dimensional incompressible viscous fluid flow in primitive variables is developed in this paper. This method combines a Galerkin variational formulation of the boundary integral equation based on single layer potential to the Stokes equation with the trial and test functions constructed by Alpert multiwavelets. Due to the use of multiwavelets and compression strategies, the present method reduces the computational complexity of system matrix from O(N²) to almost O(N) (where N is the number of unknowns). In order to compute the double integrals with logarithmic kernel more efficiently, the analytical formulae to calculate the inner integrals are presented in this paper and then the Gaussian quadrature is used for the outer integrals. Some numerical examples are given to demonstrate the availability of the method.     

M带平衡多小波

对M带多小波,引入了p阶平衡概念.从时域角度给出了M带多小波的p阶平衡条件,并就不平衡的多小波,给出了对M带多小波进行平衡的统一算法.     

A class of finite element methods based on orthonormal,compactly supported wavelets

This paper develops a class of finite elements for compactly supported, shift-invariant functions that satisfy a dyadic refinement equation. Commonly referred to as wavelets, these basis functions have been shown to be remarkably well-suited for integral operator compression, but somewhat more difficult to employ for the representation of arbitrary boundary conditions in the solution of partial differential equations. The current paper extends recent results for treating periodized partial differential equations on unbounded domains in R ⁿ, and enables the solution of Neumann and Dirichlet variational boundary value problems on a class of bounded domains. Tensor product, wavelet-based finite elements are constructed. The construction of the wavelet-based finite elements is achieved by employing the solution of an algebraic eigenvalue problem derived from the dyadic refinement equation characterizing the wavelet, from normalization conditions arising from moment equations satisfied by the wavelet, and from dyadic refinement relations satisfied by the elemental domain. The resulting finite elements can be viewed as generalizations of the connection coefficients employed in the wavelet expansion of periodic differential operators. While the construction carried out in this paper considers only the orthonormal wavelet system derived by Daubechies, the technique is equally applicable for the generation of tensor product elements derived from Coifman wavelets, or any other orthonormal compactly supported wavelet system with polynomial reproducing properties.Research supported in part by NASA Langley Research Center, Computational Structural Mechanics Branch, Jerry Housner     

旋转机械故障诊断的多小波分析法

本文选择 Daubechies、Coiflets、Symlets、Biorthogonal等多小波 ,对叠加有白噪声的典型旋转机械故障信号进行多分辨分析、比较 ,给出了不同分辨率下的离散近似 ,结果表明多小波比单一小波较容易而准确地获得故障特征信息     

Mechanically based models: Adaptive refinement for B‐spline finite element

This article presents two new methods for adaptive refinement of a B‐spline finite element solution within an integrated mechanically based computer aided engineering system. The proposed techniques for adaptively refining a B‐spline finite element solution are a local variant of np‐refinement and a local variant of h‐refinement. The key component in the np‐refinement is the linear co‐ordinate transformation introduced into the refined element. The transformation is constructed in such a way that the transformed nodal configuration of the refined element is identical to the nodal configuration of the neighbour elements. Therefore, the assembly proceeds as with classic finite elements, while the solution approximation conforms exactly along the inter‐element boundaries. For the h‐refinement, this transformation is introduced into a construction that merges the super element from the finite element world with the hierarchical B‐spline representation from the computational geometry. In the scope of developing sculptured surfaces, the proposed approach supports C⁰ as well as the Hermite B‐spline C¹ continuous shapes. For sculptured solids, C⁰ continuity only is considered in this article. The feasibility of the proposed methods in the scope of the geometric design is demonstrated by several examples of creating sculptured surfaces and volumetric solids. Numerical performance of the methods is demonstrated for a test case of the two‐dimensional Poisson equation. Copyright © 2003 John Wiley & Sons, Ltd.     

完全重构的双正交滤波带

给出了由已知的双正交矩阵滤波带BMFs构造出许多新的双正交矩阵多滤波带的方法。且有如果已知的BMFs,满足完全重构条件,则构造出来的BMFs也满足完全重构条件,另外,我们也可以从低阶BMFs构造更高阶BMFs。从数学的观点来看,这种变换可能会改变多尺度函数的支撑区间,正则性和逼近阶,然而将原始的和构造出来的BMFs应用到信号处理中,却可以得到相同的输出信号。