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Student Number 85221006
Author Ke-Ying Su(蘇哿穎)
Author's Email Address No Public.
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Department Mathematics
Year 1997
Semester 2
Degree Master
Type of Document Master's Thesis
Language zh-TW.Big5 Chinese
Title The Wavelet-Finite element solution and the stability analysis for Helmholtz equations
Date of Defense 0000-00-00
Page Count 44
Keyword
  • finite element method
  • Helmholtz
  • wavelet
  • Abstract During the last several decades, Helmholtz equation has
    played animportant role in engineering, as medical diagnostics,
    non-destructiveindustrial testing, anti-submarine warfare, oil
    exploration, etc. First, we learn some characters of mathematics
    and physics for Helmholtz equation,then find the numerical
    solution by finite element method and Wavelet -Galerkin method.
    From some papers, we know that, we will get a discrete
    wavebumber $k'$in the process of solving Helmholtz equation by
    using finite element method;$|k-k'|$ is called phase difference.
    By the phase difference, we can explainthe curve in the figure
    of $H^1$-seminorm relative error. There are moredetails in the
    chapter 3.  In the chapter 4, we solve the periodic Helmholtz
    equation by Wavelet-Galerkin method. We use Daubechies'
    orthonormal scaling functions $phi (x)$and elevated scaling
    functions $Phi (x)=int_{-infty}^xphi (t)-phi (t-1),dt$ as
    the basis function. The experiments show that they have the
    sameerror estimate as finite element method. These tall us that
    we can use the decomposition and restruction of (elevated)
    wavelet to reduce the condition number of stiffness matrix.
    Table of Content 第一章 導論 1
    第二章 數學模型 5
    第一節 解的性質 6
    第二節 變分式和弱解 7
    第三節 基本解 9
    第三章 有限元解 12
    第一節 離散數值解 12
    第二節 H1-seminorm誤差估計 15
    第三節 L2-norm誤差估計 24
    第四章 Wavelet-Galerkin方法 27
    第一節 從Fourier分析到Wavelet分析 27
    第二節 正則凌波函數的一些性質 31
    第三節 Helmholtz方程週期解 35
    第四節 提昇凌波函數 40
    參考文獻 43
    Reference 1. F.Ihelnburg and I.Babuska, 'Finite element solution to Helmholtz equation with high wavenumber -part I: The h-version of FEM', Compo Math. Appl., 30(9), 9-37(1995).
    2. F.Ihelnburg and I.Babuska, 'Finite element solution to Helmholtz equation with high wavebumber -part II: The hp-version of FEM', SIAM J. Numer. Anal., 34(1), 315358(1997).
    3. F.Ihelnburg and I.Babuska, 'Dispersion analysis and error estimation of Galerkin finite element methods for Helmholtz equation', Internat. J. Numer. Methods Engrg., 38, 3745-3774(1995).
    4. A.K.Aziz, R.B.Kellogg and A.B.Stephens, 'A two point boundary value problem with a rapidly oscillating solution', Numer. Math., 53, 107-121(1988).
    5. J.Douglas Jr., J.E.Santos, D.Sheen and L.Schreiyer, 'Frequency domain treatment of one-dimension scalar wave', Math. Models and Methods in Appl. Sci., 3(2),171194(1993).
    6. A.Zemla, 'On the fundamental solutions for the difference Helmholtz operator', SIAM J. Numer. Anal., 32(2), 560-570(1995).
    7. F.John, Partial Differential Equations, Fourth edition, Springer, New York, (1982).
    8. G.Strang and T.Nguyen, Wavelets and Filter Banks, Wellesley-Cambridge Press, (1996).
    9. I.Daubechies, Ten Lectures on Wavelets, SIAM, Philadelphia, (1992).
    10. W.-C.Shann and C.-C.Yan, 'Quadratrues involving polynomials and Daubechies' wavelets', Technical Report 9301, Department of Mathematics, National Central University, (1993).
    11. S.C.Brenner and L.R.Scott, The Mathematical Theory of Finite Element Methods, Springer, New York, (1994).
    12. G.Chen and J.Zhou, Boundary Element Methods, Academic Press Limited, London, (1992).
    13. N.I.Achieser, Vorlesungen iiber Approximations Theory, Akademieverlag, Berlin, (1953).
    14. G.Strang and G.J.Fix, An Analysis of the Finite Element Method, Prentice Hall, Englewood Cliffs, N.J, (1973).
    15. A.Cohen and R.D.Ryan, Wavelets and Multiscale Signal Pricessing, Chapman & Hall, London, (1995).
    16. G.Birkhoff and G.C.Rota, Ordinary Differential Equations, Fourth Edition, John Wiley & Sons, Singapore, (1989).
    17. 嚴健彰,"凌波理論",中央大學數學系碩士論文,(1995).
    18. 曾正男,"一套提昇凌波函數逼近能力與平滑度的方法",中央大學數學系碩士論文,(1997).
    19. A.Bayliss, C.I.Goldstein and E.Turkel, 'On accuracy conditions for the numerical computation of waves', J. Compo Phys., 59, 396-404(1985).
    Advisor
  • Shann Wei-Chang(單維彰)
  • Files No Any Full Text File.
    Date of Submission

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