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研究生:柯妙珍
研究生(外文):Miao-Chen Ke
論文名稱:非線性SOR及網格重新分佈之探討
論文名稱(外文):Nonlinear SOR and Mesh Redistribution
指導教授:陳慈芬
指導教授(外文):Tsu-Fen Chen
學位類別:碩士
校院名稱:國立中正大學
系所名稱:應用數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2001
畢業學年度:89
語文別:英文
論文頁數:51
中文關鍵詞:非線性SOR網格重新分配
外文關鍵詞:Nonlinear SORGrading Functionmesh redistributionGeneralized Newton's MethodStrictly convex functional
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摘 要
這篇論文主要討論之問題,是在求嚴格凸泛函的極小值。這裡利用有限元素法將問題離散化,再用非線性SOR解非線性方程組。為了加速非線性SOR的收斂性及準確性,考慮加入重新分配格點的函數來配合計算。結果顯示出這個作法的確可以改進非線性SOR的收斂速度及得到較精準的解。這個作法的應用範圍及限制性,都將在這論文裡討論。

In order to speed up the rate of convergence for nonlinear SOR to solve the problems of minimizing strict convex functionals, this article is concerned with the construction of an appropriate grading of a mesh for nonlinear SOR. The functionals are discretized by finite element methods and the
convergence of the discretization is guaranteed. Numerical results of the models problems illustrating the efficiency and accuracy are presented. Discussions of the capabilities and limitations of the approaches are also provided.

1. Introduction --------------------------------------------- 2
2. Nonlinear SOR -------------------------------------------- 3
3. Convergence Results of Nonlinear ------------------------- 4
4. SORGrading Functions and Optimal mesh --------------------14
5. Numerical results and discussions ------------------------17

[1] M.E. Brewster and R.Kannan, Nonlinear Successive
Over-Relaxation, Numerische Math. 44(1984) 309-315.
[2] M.E. Brewster and R.Kannan, Gobal Convergence of Nonlinear Successive Over-Relaxation via Linear Theory, Computing 34(1985) 73-79.
[3] M.E. Brewster and R.Kannan, A computional Process for Choosing the Relaxation Parameter in Nonlinear SOR, Computing 37(1986) 19-29.
[4] Tsu-Fen Chen and R.Kannan, Grid Refinement and Nonlinear SOR, Journal of Nonlinear Functional Analysis and Optimization, Vol 22, No.3(2001).
[5] Tsu-Fen Chen, G.J.Fix and H.D. Yang, Numerical Studies of Optimal Grid Construction, Numer. Methods Partial Different. Eq. 12(1996) 191-206.
[6] G.F. Carey and H.T. Dinh, Grading Functions and Mesh Redistribution, Siam J. Numer. Anal. 22(1985) 1028-1040.
[7] D.Greenspan, On Approximating Extremals of Functions, I. The Method and Examples for Boundary Value Problems, Bull.ICC4(1965) 99-120.
[8] T.Tsuchiya, On Two Methods for Approximating Minimal Surfaces in Parametric Form, Math. Comp. 46(1986) 517-529.

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