基于区间三次Hermite样条小波的Poisson方程数值求解方法

向家伟; 陈雪峰; 李锡夔

doi:10.3879/j.issn.1000-0887.2009.10.012

基于区间三次Hermite样条小波的Poisson方程数值求解方法

doi: 10.3879/j.issn.1000-0887.2009.10.012

1.
桂林电子科技大学机电工程学院,广西桂林 541004;
西安交通大学机械制造系统工程国家重点实验室,西安 710049;
大连理工大学工业装备结构分析国家重点实验室,辽宁大连116024

基金项目: 国家自然科学基金资助项目(50805028;50875195);工业装备结构分析国家重点实验室开放课题基金资助项目(GZ0815)

详细信息

作者简介:
向家伟(1974- ),男,湖南辰溪人,副教授,博士(联系人.E-mail:wxw8627@163.com).

中图分类号: O351.2
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- 被引次数: 0
出版历程
- 收稿日期: 2009-05-05
- 修回日期: 2009-08-23
- 刊出日期: 2009-10-15

Numerical Solution of Poisson Equation by Using Wavelet Bases of Hermite Cubic Splines on the Interval

1.
School of Mechantronic Engineering, Guilin University of Electronic Technology Guilin, Guangxi 541004, P. R. China;
State Key Laboratory for Manufacturing Systems Engineering, Xi'an Jiaotong University, Xi'an 710049, P. R. China;
State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, Liaoning 116024, P. R. China

摘要

摘要: 提出一种新的求解Poisson方程的小波有限元方法，采用区间三次Hermite样条小波基作为多尺度有限元插值基函数，并详细讨论了小波有限元提升框架．由于小波基按照给定的内积正交，可实现相应的多尺度嵌套逼近小波有限元求解方程，在不同尺度上的插值基之间完全解耦和部分解耦．数值算例表明在求解Poisson方程时，该方法具有高的效率和精度．
- Poisson方程 /
- 三次Hermite样条小波 /
- 提升框架 /
- 小波有限元方法
Abstract: A new wavelet-based finite element method was proposed for solving Poisson equation. The wave let bases of Hermite cubic splines on the in terval were employed as the multi-scale in terpo lating basis for finite element analysis. The lifting scheme of wavele-tbased finite element method was discussed in details. For the orthogral characteristic of the wavelet bases with respect to the given inner product, the correspond ing multi-scale finite element equation will be decoupled across scales to tally or partially and be suited for nesting approx mi ation. Some num erica l exam p les ind icate that the p roposed method has higher efficiency and precision in solving Poisson equation.
- Poisson equation /
- Hermite cubicsplines wavele /
- lifting scheme /
- wavelet finite element method

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参考文献(16)

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