Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/17496
標題: 多重網格-共軛梯度法處理反應-擴散系統
Multigrid-conjugate gradient type methods for reaction-diffusion systems
作者: 陳慧霜
Chen, Jessica
關鍵字: 反應-擴散系統
reaction-diffusion systems
延續法
分歧點
有限差分法
多重網格法
continuation methods
bifurcation
finite differenes
multigrid methods
Bi-CGSTAB
GMRES
出版社: 應用數學系
摘要: 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.
URI: http://hdl.handle.net/11455/17496
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