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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

向家伟, 陈雪峰, 李锡夔. 基于区间三次Hermite样条小波的Poisson方程数值求解方法[J]. 应用数学和力学, 2009, 30(10): 1243-1250. doi: 10.3879/j.issn.1000-0887.2009.10.012
引用本文: 向家伟, 陈雪峰, 李锡夔. 基于区间三次Hermite样条小波的Poisson方程数值求解方法[J]. 应用数学和力学, 2009, 30(10): 1243-1250. doi: 10.3879/j.issn.1000-0887.2009.10.012
XIANG Jia-wei, CHEN Xue-feng, LI Xi-kui. Numerical Solution of Poisson Equation by Using Wavelet Bases of Hermite Cubic Splines on the Interval[J]. Applied Mathematics and Mechanics, 2009, 30(10): 1243-1250. doi: 10.3879/j.issn.1000-0887.2009.10.012
Citation: XIANG Jia-wei, CHEN Xue-feng, LI Xi-kui. Numerical Solution of Poisson Equation by Using Wavelet Bases of Hermite Cubic Splines on the Interval[J]. Applied Mathematics and Mechanics, 2009, 30(10): 1243-1250. 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
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

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

  • 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.
  • [1] Canuto C, Tabacco A, Urban K. The wavelet element method part I: construction and analysis[J]. Applied and Computational Harmonic Analysis, 1999, 6(1):1-52. doi: 10.1006/acha.1997.0242
    [2] Canuto C, Tabacco A, Urban K. The wavelet element method part II: realization and additional feature in 2D and 3D[J]. Applied and Computational Harmonic Analysis, 2000, 8(2): 123-165. doi: 10.1006/acha.2000.0282
    [3] Cohen A. Numerical Analysis of Wavelet Method[M]. Elsevier: Amsterdam, 2003, 20-29.
    [4] 周又和, 王记增, 郑晓静. 小波伽辽金有限元法在梁板结构中的应用[J]. 应用数学和力学, 1998, 19(8): 697-706.
    [5] Chen X F, He Z J, Xiang J W, Li B. A dynamic multiscale lifting computation method using Daubechies wavelet[J]. Journal of Computational and Applied Mathematics, 2006, 188(2): 228-245. doi: 10.1016/j.cam.2005.04.015
    [6] Xiang J W, Chen X F, He Z J, et al. The construction of 1D wavelet finite elements for structural analysis[J]. Computational Mechanics, 2007, 40(2): 325-339. doi: 10.1007/s00466-006-0102-5
    [7] Xiang J W, Chen X F, He Z J, et al. A new wavelet-based thin plate element using B-spline wavelet on the interval[J]. Computational Mechanics, 2008, 41(2): 243-255.
    [8] Xiang J W, Chen X F, Yang L F, et al. A class of wavelet-based flat shell elements using B-spline wavelet on the interval and its applications[J]. CMES-Computer Modeling in Engineering and Sciences, 2008, 23(1):1-12.
    [9] 梅树立, 陆启韶, 金俐,等. 偏微分方程的区间小波自适应精细积分法[J]. 应用数学和力学, 2005, 26(3): 364-371.
    [10] 金坚明, 薛鹏翔, 徐应祥,等. 具有紧支撑的非张量积形式二维小波有限元[J]. 应用数学和力学, 2006, 27(12): 1673-1686.
    [11] 贺英, 韩波. 流体饱和多孔隙介质波动方程小波有限差分法[J]. 应用数学和力学, 2008; 29(11): 1495-1504.
    [12] Basu P K, Jorge A B, Badri S, et al. Higher-order modeling of continua by finite-element, boundary-element, Meshless, and wavelet methods[J]. Computers and Mathematics With Applications. 2003, 46(1): 15-33.
    [13] Jia R Q, Liu S T. Wavelet bases of Hermite cubic splines on the interval[J]. Advances in Computational Mathematics, 2006, 25(1/3): 23-39. doi: 10.1007/s10444-003-7609-5
    [14] Quak E, Weyrich N. Decomposition and reconstruction algorithms for spline wavelets on a bounded interval[J]. Applied and Computational Harmonic Analysis, 1994, 1(2): 217-231. doi: 10.1006/acha.1994.1009
    [15] Dahmen W, Kurdila A, Oswald P. Multiscale Wavelet for Partial Differential Equations[M]. San Diego:Academic Press,1997, 23-27.
    [16] Pavel K, Anath F, Pinhas Z, et al. Mechanically based models adaptive refinement for B-spline finite element[J]. International Journal for Numerical Methods in Engineering, 2003, 57(8):1145-1175. doi: 10.1002/nme.717
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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

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