Wavelet Algorithm for the Numerical Solution of Plane Elasticity Problem

  • Youjian Shen
  • Wei Lin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2251)


In this paper, we apply Shannon wavelet and Galerkin method to deal with the numerical solution of the natural boundary integral equation of plane elasticity probem in the upper half-plane. The fast algorithm is given and only 3K entries need to be computed for one 4K × 4K stiffness matrix.


plane elasticity problem natural integral equation Shannon wavelet Galerkin-wavelet method 


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  1. 1.
    W. Lin, Y. J. Shen, Wavelet solutions to the natural integral equations of the plane elasticity problem, Proceedings of the second ISAAC Congress, Vol. 2, 1471–1480. (2000), Kluwer Academic Publishers.Google Scholar
  2. 2.
    Dehao Yu, Mathematical theory of natural boundary element methods, Science press (in chinese), Beijing (1993).Google Scholar
  3. 3.
    K. Feng and D. Yu, Canonical integral equations of elliptic boundary value problems and their numerical solutions, Proc. of China-France Symp. on FEM, Science Press, Beijing (1983), 211–252.Google Scholar
  4. 4.
    Wensheng Chen and Wei Lin, Hadamard singular integral equations and its Hermite wavelet, Proc. of the fifth international colloquium on finite or infinite dimensional complex analysis, (Z. Li, S. Wu and L. Yang. Eds.) Beijing, China (1997), 13–22.Google Scholar
  5. 5.
    C.-Y. Hui, D. Shia, Evaluations of hypersingular integrals using Gaussian quadrature, Int. J. for Numer. Meth. in Engng. 44, 205–214 (1999).zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    R. P. Gilbert and Wei Lin, Wavelet solutions for time harmonic acoutic waves in a finite ocean, Journal of Computional Acoustic Vol. 1, No. 1 (1993) 31–60.CrossRefMathSciNetGoogle Scholar
  7. 7.
    C. A. Micchelli, Y. Xu and Y. Zhao, Wavelet Galerkin methods for second-kind integral equations. J. Comp. Appl. Math. 86 (1997), 251–270.zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Tobias Von Petersdor., Christoph Schwab, Wavelet approximations for first kind boundary integral equations on polygons, Numer, Math, 74 (1996), 479–519.CrossRefMathSciNetGoogle Scholar
  9. 9.
    I. Daubechies, Ten lectures on wavelets, Capital City Press, Montpelier, Vermont, 1992.zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Youjian Shen
    • 1
  • Wei Lin
    • 2
  1. 1.Department of MathematicsZhongshan University and Hainan Normal UniversityHaikouP. R. China
  2. 2.Department of MathematicsZhongshan UniversityGuangzhouP. R. China

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