Title page for 952201005


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Student Number 952201005
Author Yu-Rong Syu(徐玉榮)
Author's Email Address ii0756@yahoo.com.tw
Statistics This thesis had been viewed 1167 times. Download 527 times.
Department Mathematics
Year 2007
Semester 2
Degree Master
Type of Document Master's Thesis
Language zh-TW.Big5 Chinese
Title The design of two-dimensional p-version finite element method using rectangular elements by C++
Date of Defense 2008-06-19
Page Count 53
Keyword
  • finite element method
  • hierarchical shape function
  • Legendre Polynomails
  • p-version finite element method
  • weak formulation
  • Abstract In this paper, we design two-dimensional p-version finite element using rectangular elements by C++. In design, we solve the following partial differential equations by using rectangular elements[sum^{n}_{l=1} { - igtriangledown cdot (A^{kl} igtriangledown u_{l}) + B^{kl} cdot igtriangledown u_{l} + C^{kl} u_{l} - igtriangledown cdot (D^{kl} u_{l}) } = f^{k} , , k = 1 cdots n]where n is the number of variables, k stands for the number of equations, so we have n equations.This paper will show the struct of program and hierarchical shape function.
    Table of Content 中文摘要. . . . . i
    英文摘要. . . . . ii
    目錄 . . . . . . . iii
    圖目錄 . . . . . . iv
    1 背景知識 . . . . . . 1
    1.1 C++物件導向程式設計 . . . . . . 1
    1.2 有限元素法基本概念 . . . . . . 2
    1.3 p-version有限元素法 . . . . . . 5
    2 Shape Function . . . . . . 6
    2.1 Shape function 基本概念與特性 . . . . . . 6
    2.2 Integrated Legendre Polynomials . . . . . . 7
    2.2.1 定義 . . . . . . 7
    2.2.2 性質 . . . . . . 7
    2.3 Hierarchical Shape Function for Quadrangle . . . . . . 8
    3 程式的類別架構與運作流程 . . . . . .14
    3.1 類別架構 . . . . . . 14
    3.1.1 Mesh 類別 . . . . . . 15
    3.1.2 Element 類別 . . . . . . 20
    3.1.3 FEM Solver 類別 . . . . . . 23
    3.1.4 Boudnary Condition 類別 . . . . . . 24
    3.1.5 Coeff 類別 . . . . . . 25
    3.1.6 Algorithm 類別 . . . . . . 27
    3.1.7 Shape Function 2D 類別 . . . . . . 29
    3.2 程式的運作流程 . . . . . . 30
    4 程式測試 . . . . . .32
    4.1 linear mesh . . . . . . 34
    4.1.1 單變數問題 . . . . . . 34
    4.1.2 雙變數問題 . . . . . . 34
    4.2 quadratic mesh . . . . . . 37
    4.2.1 單變數問題 . . . . . . 37
    4.2.2 雙變數問題 . . . . . . 37
    5 範例 . . . . . .40
    5.1 Time Independent Stokes Equations . . . . . . 40
    5.2 Time Independent Navier-Stokes Equations . . . . . . 42
    5.3 Time Dependent Navier-Stokes Equations . . . . . . 46
    5.4 p-version . . . . . . 49
    6 結論 . . . . . .51
    參考文獻 . . . . . . 52
    Reference [1] Bjarne Stroustrup 著,葉秉哲譯,C++程式語言經典本(The C++ Programing
    Language, 3rd ed.) 儒林發行,1999
    [2] Linda M. Northrop 著, 物件導向的軟體發展,
    http://tropic.iis.sinica.edu.tw/sofeeng/sofeeng 8.htm
    [3] 子由著,深度學習C++(第二版) 博碩發行,2006
    [4] W.H. Wu, An object-oriented design of multiregion, structured / unstructured
    grid generation in C++ , Department of Mathematics, National Central University,
    Taiwan, library note
    [5] Barna Szabo & Ivo Babuska, Finite Element Analysis , A Wiley-Interscience
    Publication, New York, 1991, pp.38-39
    [6] Barna Szabo and Ivo Babuska, Finite Element Analysis , A Wiley-Interscience
    Publication, New York, 1991
    [7] 梁坤善,在二維空間上使用三角形元素的p-version有限元素法程式設計,
    中央大學數學系碩士論文,2008
    [8] David Kincaid & Ward Chenney, Numerical analysis: mathematics of scientific
    computing Third, Brooks/Cole, USA, 2002, 539-546
    [9] Eric B. Becker, Graham F. Carey, & J. Tinsley Oden, FINITE ELEMENTS
    An Introduction, Prentice-Hall, USA, 1981
    [10] Vithal A. Patel, Numerical Analysis, Thomson Learning, Asia, 2001, 81-86
    [11] David Vandevoorde & Nicolai M. Josuttis 著, 侯捷, 榮耀& 姜宏譯, C++
    Templates全覽(C++ templates : the complete guide), 眳p, 2004
    [12] Matthew H. Austern 著, 黃俊堯& 侯捷譯, 泛型程式設計與STL(Generic
    programming and the STL), 眳p, 2001
    [13] Avner Friedman, Foundations of Modern Analysis, Dover Publications, Inc. ,
    New York, 95-98
    Advisor
  • Wei-Han Wu(吳維漢)
  • Files
  • 952201005.pdf
  • approve immediately
    Date of Submission 2008-06-27

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