臺灣博碩士論文加值系統

我們討論多重網格法應用在延續法中，來解非線性橢圓特徵值問題。我們使用有限元素法來離散化這些問題，且在多重網格法的V-循環，W-循環以及完全的多重網格V-循環中，使用Lanczos法作為其中的鬆弛法。我們提供一些多重網格延續演算法找出非線性橢圓特徵值問題的曲線。由數值的結果證明我們提供的演算法是有效的。最後我們將所得結果繪製成圖表並做結論。

We study multigrid methods in the context of continuation methods for nonlinear elliptic eigenvalue problems. Here we use the finite element method to discretize the problems. The Lanczos method is used as the relaxation scheme for the V-cycle, W-cycle and full multigrid V-cycle schemes, respectively. Some multigrid-continuation algorithms are proposed for tracing the solution curves in the nonlinear elliptic eigenvalue problems. Our numerical results show the algorithms we propose are efficient. Finally, some concluding remarks are given.

1.Introduction 1
2.A brief review of the Lanczos type algorithms 2
3.Continuation and local perturbation 3
4.The finite-element method 6
5.V-cycle, W-cycle and full multigrid V-cycle methods 8
6.Numerical results 12
7.Conclusions 14
List of tables 15
List of figures 18
References 27

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