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研究生:陳慧霜
研究生(外文):Jessica Chen
論文名稱:多重網格-共軛梯度法處理反應-擴散系統
論文名稱(外文):Multigrid-conjugate gradient type methods for reaction-diffusion systems
指導教授:簡澄陞
指導教授(外文):Cheng-Sheng Chien
學位類別:碩士
校院名稱:國立中興大學
系所名稱:應用數學系
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:2002
畢業學年度:90
語文別:中文
論文頁數:31
中文關鍵詞:反應-擴散系統延續法分歧點有限差分法多重網格法
外文關鍵詞:reaction-diffusion systemscontinuation methodsbifurcationfinite differenesmultigrid methodsBi-CGSTABGMRES
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  • 被引用被引用:0
  • 點閱點閱:211
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我們利用多重網格法在延續法中處理反應-擴散系統,在多重網格法的V循環、W循環和滿近似法中,分別使用Bi-CGSTAB法和GMRES法作為其中的鬆弛法。我們特別應用Brown和Walker的結果來研究GMRES法如何被使用來解延續問題中產生的近似奇異系統。我們證明為了安全地轉換分支目的,而去解靠近分歧點的干擾問題。非線性橢圓特徵值問題中,我們提出幾個多重網格-延續法的演算法來處理非線性曲線的軌道。由數值結果顯示出,我們提出的演算法是強壯的而且可以很容易地執行。

We study multigrid methods in the context of continuation methods for reaction-diffusion systems, where the Bi-CGSTAB and the GMRES methods are used as the relaxation scheme for the V-cycle, W-cycle and full approximation schemes, respectively. In particular, we apply the results of Brown and Walker [1997] to investigate how the GMRES method can be used to solve nearly singular systems that occur in continuation problems. We show that for the sake of switching branches safely, one would rather to solve a perturbed problem near bifurcation points. We propose several multigrid-continuation algorithms for curve-tracking in nonlinear elliptic eigenvalue problems. Our numerical results show that the algorithms we propose have the advantage of being robust and can be easily implemented.

1.Introduction...............................................2
2.A brief review of the GMRES and the Bi-CGSTAB algorithms...4
3.Solving nearly singular linear systems.....................8
4.Some multigrid-GMRES (Bi-CGSTAB) algorithms................11
5.Numerical results..........................................17
6.Conclusions................................................19
Tables.......................................................20
Figures......................................................23
References...................................................30

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