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论文作者:英语论文网论文属性:论文指导登出时间:2013-08-15编辑:zbzbz点击率:3370
论文字数:768论文编号:org201308141738458611语种:英语 English地区:英国价格:免费论文
摘要:有限元分析是工程研究的主要方法之一,在留学生论文中该方法经常提及,因此,通过一篇范文使大家掌握如何写好该类论文,能够旅顺写作思路。
A study of multiscale wavelet-based elements for adaptive finite element analysis
多尺度小波基单元的自适应有限元分析探究
1. Introduction
Algorithms issued from the wavelet numerical method have been used in many situations and with different discretizations for the resolution of some mathematical and physical partial differential equations (PDEs). The wavelet numerical methods embody two prominent advantages . The one is that the scale is directly upgraded by using the so called two scale equations, namely, the scaling functions at different scale are employed directly to form the multiscale approximation basis. The other is that the nesting approximation is performed by using the lifting relationship between scale and wavelet spaces, i.e. the scaling functions
and wavelets at certain scale are adopted to form the scaling function at next scale. Therefore, wavelet numerical methods are well argued by many researchers not only in numerical analysis domains but also in structural analysis fields.
1。景区简介
从小波数值方法发布算法已经应用在许多情况下,不同的离散数学和物理的一些偏微分方程(PDE)的分辨率。小波数值方法体现的两个突出的优点。一是规模直接升级使用所谓的双尺度方程,即,缩放功能在不同的尺度是直接采用,形成多尺度逼近的基础上。二是嵌套逼近进行提升小波空间之间的关系,即缩放功能在一定尺度小波尺度函数采用的形式在下表。因此,小波数值方法以及辩称,不仅在数值分析领域的许多研究人员也在结构分析领域。
In accordance with the first prominent advantages of wavelet numerical methods, recently, two-dimensional Daubechies wavelet-based element for a thin plate-bending problem had been constructed by Chen. For Daubechies wavelet lacking of explicit expressions, the calculation of integral has some difficulties. Han proposed multivariable wavelet-based finite element method using C0 type interpolating wavelet to analyze the thick plate. Also, Han constructed some spline wavelet elements for analyzing structural mechanics problems. Those elements were built up in the theory of spline wavelet. Xiang successfully constructed one-dimensional wavelet-based elements and two-dimensional plane elastomechanics and Mindlin plate elements by using B-spline wavelet on the interval (BSWI). Moreover, Xiang employed BSWI scaling functions as approximation functions for solving thin plate bending and vibration problems with good performances.
根据小波数值方法,第一个突出优点,近年来,二维Daubechies小波单元对薄板弯曲问题被陈构造。缺乏对Daubechies小波的显式表达式,定积分的计算有一定的困难。寒]提出的多变量小波使用C0型插值小波分析厚板有限元法。同时,汉[ 8 ]建立了样条小波元分析结构力学问题。这些元素在样条小波理论的建立。乡成功构建了基于小波变换的元素和一维二维平面弹性力学Mindlin板单元利用区间B样条小波(BSWI)。此外,乡采用区间B样条小波尺度函数作为逼近函数求解薄板弯曲和振动问题具有良好的性能。
For the nesting approximation of wavelet numerical methods, in the current literatures, the whole domain discretization method was widely used. Martin and Michel made a full investigation about convergence of an adaptive semi-Lagrangian scheme for the Vlasov–Poisson system [12] . Wavelet-based adaptive Galerkin discretization method was verified to be a robust way to solve elliptic PDE’s on product domains [13] . Dijkema, Christoph and Rob also proposed an adaptive wavelet method for solving high-dimensional elliptic PDEs, such as Poisson’s equation and the wavelet-based approximations converge in energy norm with the same rate as the best approximations form the span of the best N tensor product wavelets[14] . The numerical performance of wave-let methods for PDEs was evaluated by Christon [15] . Some com-ments were also given by the author, i.e. the design of wavelet bases that are customized for a specific本论文由英语论文网提供整理,提供论文代写,英语论文代写,代写论文,代写英语论文,代写留学生论文,代写英文论文,留学生论文代写相关核心关键词搜索。