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Numerical solution of Poisson equation with wavelet bases of Hermite cubic splines on the interval

  • Jia-wei Xiang (向家伟)Email author
  • Xue-feng Chen (陈雪峰)
  • Xi-kui Li (李锡夔)
Article

Abstract

A new wavelet-based finite element method is proposed for solving the Poisson equation. The wavelet bases of Hermite cubic splines on the interval are employed as the multi-scale interpolation basis in the finite element analysis. The lifting scheme of the wavelet-based finite element method is discussed in detail. For the orthogonal characteristics of the wavelet bases with respect to the given inner product, the corresponding multi-scale finite element equation can be decoupled across scales, totally or partially, and suited for nesting approximation. Numerical examples indicate that the proposed method has the higher efficiency and precision in solving the Poisson equation.

Key words

Poisson equation Hermite cubic spline wavelet lifting scheme wavelet-based finite element method 

Chinese Library Classification

O351.2 

2000 Mathematics Subject Classification

65T60 65L05 35F30 

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Copyright information

© Shanghai University and Springer Berlin Heidelberg 2009

Authors and Affiliations

  • Jia-wei Xiang (向家伟)
    • 1
    • 2
    Email author
  • Xue-feng Chen (陈雪峰)
    • 2
  • Xi-kui Li (李锡夔)
    • 3
  1. 1.Faculty of Mechanical and Electrical EngineeringGuilin University of Electronic TechnologyGuilinP. R. China
  2. 2.State Key Laboratory for Manufacturing Systems EngineeringXi’an Jiaotong UniversityXi’anP. R. China
  3. 3.State Key Laboratory of Structural Analysis for Industrial EquipmentDalian University of TechnologyDalianP. R. China

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