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Student Number 85221006 Author Ke-Ying Su(蘇哿穎) Author's Email Address No Public. Statistics This thesis had been viewed 349 times. Download 15 times. 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

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