標題: ㄧ個新密度泛函理論推導公式之三維有限元素解
3D finite element solution of a new formulation in density functional theory
作者: 蔡維哲
Wei-Che Tsai
劉晉良
Jinn-Liang Liu
應用數學系所
關鍵字: 有限元素法;密度泛函理論;自洽;薛丁格方程;普瓦松方程;Finite Element Method;Density Functional Theory;Kohn Sham Equation;Jacobi-Davidson Method;Preconditioned Conjugate Gradient;self-consistence;Schrodinger Equation;Poisson Equation
公開日期: 2004
摘要: 在這一篇論文中有二個部分。在第一個部分裡,我們主要探討電子限制在量子奈米結構中的情況。我們主要學習使用self-consistence迭代方式來處理一個非線性偏微分系統,這系統是由普瓦松方程式與薛丁格方程式共同組成。藉由這個非線性偏微分系統來描述電子在量子奈米結構中的變化。在第二個部分裡,我們嘗試使用許正餘教授在密度泛函理論所推導出來一個新的公式,從這新的公式出發,使用有限元素法希望能夠得到電子在原子與分子結構中很好的描述,我們在處理這問題同時,也嘗試學習使用更有效率的數值方法來處理有限元素法整理出來的大型矩陣。
There are two parts in the thesis. In the first part, we discuss that electrons confine in quantum nanostructures. We use self-consistence iteration method for solving the nonlinear PDE system. The system consists of Poisson equation and Schrodinger equation. It describes the electronic changes in quantum nanostructures by the nonlinear PDE system. In the second part, we try to compute a new formulation derived by Prof. Hsu. From the formulation, we hope to get good numerical results by using finite element method. The main goal of this thesis is to simulate electronic properties of well-known atomic models by using our still under development finite element codes for future research on density functional theory.
URI: http://140.113.39.130/cdrfb3/record/nctu/#GT009222517
http://hdl.handle.net/11536/76368
Appears in Collections:Thesis


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