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標題: 雙重網格離散法處理非線性薛丁格-波松系統
Two-grid discretization methods for nonlinear Schrdinger-Poisson system
作者: 林進一
Lin, Chin-Yi
關鍵字: Two-grid centered difference method
continuation method
Schrdinger eigenvalue problem
Schrdinger-Poisson system
semilinear elliptic eigenvalue problems
出版社: 應用數學系
摘要: 我們提出新的雙重網格中央差分法處理邊界為週期之自伴偏微分運算子的最小特徵對偶問題。典型之例子為薛丁格特徵值問題。此問題一般具有重複和聚集的特徵值。利用此方法,我們發展出新的雙重網格中央差分法處理非線性薛丁格-波松特徵值問題的數值解。我們的數值結果顯示出在考慮薛丁格-波松系統下,薛丁格特徵值問題的前幾個少數之特徵對偶如何被雜質影響。接著,我們提出一些變異的雙重網格中央差分離散法找出半線性橢圓特徵值問題的分支解。在考慮運算方程的線性近似下,我們主要在細網格執行精確和不精確的修正。並提出一些實例數值的結果。
We present a new implementation of the two-grid centered difference method for computing extremum eigenpairs of self-adjoint partial differential operators with periodic boundary conditions, which in general possess multiple and clustered eigenvalues. One typical example is the Schrdinger eigenvalue problem. Based on this method we develop a novel two-grid centered difference method for the numerical solutions of the nonlinear Schrdinger-Poisson eigenvalue problem. Our numerical results show how the first few eigenpairs of the Schrdinger eigenvalue problem are affected by the dopant which is considered in the Schrdinger-Poisson system. Next, we present some variants of the two-grid centered difference discretization schemes for tracing solution branches of semilinear elliptic eigenvalue problems. We mainly perform exact and inexact corrections on the fine grid by considering linear approximations of operator equations. Sample numerical results are reported.
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