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Applied Mathematics and Mechanics (English Edition) ›› 2009, Vol. 30 ›› Issue (10): 1325-1334.doi: https://doi.org/10.1007/s10483-009-1012-x

• Articles • 上一篇    下一篇

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

向家伟1,2 陈雪峰2 李锡夔3   

  1. 1. Faculty of Mechanical and Electrical Engineering, Guilin University of Electronic Technology, Guilin 541004, P. R. China;
    2. State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an 710049, P. R. China;
    3. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, P. R. China
  • 收稿日期:2009-04-29 修回日期:2009-08-23 出版日期:2009-10-01 发布日期:2009-10-01

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

 XIANG Jia-Wei1,2, CHEN Xue-Feng2, LI Xi-Kui3   

  1. 1. Faculty of Mechanical and Electrical Engineering, Guilin University of Electronic Technology, Guilin 541004, P. R. China;
    2. State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an 710049, P. R. China;
    3. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, P. R. China
  • Received:2009-04-29 Revised:2009-08-23 Online:2009-10-01 Published:2009-10-01

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摘要： 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.

关键词: Poisson equation, Hermite cubic spline wavelet, lifting scheme, waveletbased finite element method

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, waveletbased finite element method

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