Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/18586
標題: 使用二重網格離散化方法解線性特徵值問題
Two-Grid Discretization Schemes for Linear Eigenvalue Problems
作者: 古嚴博
Gu, Yen-Po
關鍵字: Linear eigenvalue problem
線性特徵值問題
Schrodinger eigenvalue problem
Generalized eigenvalue problem
block Lanczos method
MINRES
SYMMLQ
Rayleigh quotient iteration
薛丁格特徵值問題
廣義特徵值問題
區塊 Lanczos 迭代法
MINRES
SYMMLQ
Rayleigh 商值迭代法
出版社: 應用數學系
摘要: 我們討論二重網格方法應用在解二階橢圓線性特徵值問題、薛丁格特徵值問題、廣義特徵值問題,其中使用中央差分法和有限元素法將這些問題離散化。此二重網格方法可以被利用於解大型的特徵值問題,而且具有重複的特徵值以及群集的特徵值。薛丁格特徵值問題在二維和三維的數值結果,證實了我們所提出的二重網格方法應用在這些問題上是有效率且堅實的。而且有限元素法比中央差分法好。
We describe two-grid discretization schemes for solving the second order linear elliptic eigenvalue problem,where both the centered difference method and the finite element method are used to discretize the PDE.These two-grid schemes can be exploited to solve large-scale eigenvalue problems with multiple and clustered eigenvalues.Numerical results on the Schrodinger eigenvalue problems in two and three dimensions shows the efficiency and robustness of the two-grid scheme we propose.
URI: http://hdl.handle.net/11455/18586
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