Please use this identifier to cite or link to this item: `http://hdl.handle.net/11455/18616`
 標題: 使用多重網格有限元素方法解非線性特徵值問題Multigrid-Finite Element Methods for Nonlinear Eigenvalue Problems 作者: 杜慧絹Tu, Hui-Juan 關鍵字: nonlinear eigenvalue problems非線性特徵值問題bifurcation pointscontinuation methodsfinite element methodmultigrid methodssymmetric linear systemsLanczos method分歧點延續法有限元素法多重網格法對稱線性系統Lanczos方法 出版社: 應用數學系 摘要: 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. URI: http://hdl.handle.net/11455/18616 Appears in Collections: 應用數學系所