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数值分析留学生论文范文:Wavelet based schemes for linear advection–dispersion equation

论文作者:英语论文网论文属性:作业 Assignment登出时间:2013-08-16编辑:zbzbz点击率:3972

论文字数:935论文编号:org201308160928002302语种:英语 English地区:英国价格:免费论文

关键词:数值分析论文留学生论文范文英国论文范文

摘要:小波技术是一个先进的数值分析技术,该技术在数值求解领域中有着广泛的应用,具有较高的数值分析效率和数值分析精度,相关的论文也得到了普遍关注,通过一个范文让留学生朋友掌握相关的写作技巧。

Wavelet based schemes for linear advection–dispersion equation

线性平流扩散方程的基于小波变换的方案


1. Introduction
Many interesting physical systems are characterized by the presence of localized structure or sharp transition, which might occur anywhere in the domain or change their locations in space with time. Popular methods such as finite element, so-called meshless and recently developed wavelet methods, to solve these problems efficiently, use adaptive grid tech-niques. Adaptive refinement techniques can also be profitably applied in solving partial differential equations useful in many applications, including simulation, animation, computer vision, etc. The currently existing adaptive grid techniques may be roughly classified as either subdivision schemes or basis refinement techniques. The major difference between these ap-proaches is that subdivision schemes solve problems in the physical space by increasing the nodes while basis refinement techniques (including hierarchical basis in finite element method) solve problems in coefficient space. Though both the adaptive grid techniques are well understood, a lot of work has to be done for efficient implementation in complex domain, in particular to reduce computational time.

1 引言

许多有趣的物理系统的特点是局部结构或尖锐过渡的存在,这可能发生在域中的任何地方或空间变化随着时间的推移,他们的位置。流行的方法,如有限元,所谓的无网格和最近开发的小波方法,有效地解决这些问题,采用自适应网格技术。自适应细化技术还可以获利的应用求解偏微分方程在许多应用中,使用包括仿真,动画,计算机视觉,等。现有的自适应网格技术大致可分为细分依据细化技术。这些方法之间的主要区别是,细分方案解决问题在物理空间的增加而细化技术节点的基础上(包括有限元法求解分层的基础上)在系数空间问题。但两者的自适应网格技术都很好理解,很多工作都是在复杂的领域,有效的实现了,特别是减少计算时间。


Wavelet has high potential for fast, hierarchical and locally adaptive algorithms because of their compactly supported refinable basis functions [1–4] . Liandrat and Tchamitchian [5] proposed the first algorithm based on a spatial approximation exploiting the regularity properties of an orthonormal wavelet basis. Beylkin and Keiser [6] used wavelet expansion for adap-tively updating numerical solution of nonlinear partial differential equations, which exhibit both smooth and shock-like behaviour. Due to the signal processing base of traditional wavelet, the research in PDE simulations [7,8] was limited to sim-ple domain and boundary conditions. This limitation has been eliminated with the development of the lifting scheme [9] and stable completion [10,11]. By using lifting scheme, Vasilyev and Paolucci [12] developed wavelet collocation method to adapt computational refinements to local demands of the solution. Krysl et al. [13] developed conforming hierarchical adap-tive refinement methods where hierarchical refinement treats refinement as the addition of finer level ‘‘detail function’’ to an unchanged set of coarse-level functions. Amaratunga and Sudarshan [14] customized the second-generation wavelets to generate hierarchical basis for finite element method to solve PDEs both hierarchically and adaptively.


Advection–dispersion equation exhibits discontinuity (shocks) after a finite time. Further, the numerical solution shows spurious oscillations when dispersion coefficient is small as compared to the velocity of flow, i.e., at high Peclet number. To capture the singular effects in the solution, the domain would require very fine resolution near singularities. The clas-sical discretization based on uniform grid will be highly uneconomical. The existing numerical techniques use artificial dispersion to overcome 论文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。

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