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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 許文翰(Wen-Hann Sheu) | |
| dc.contributor.author | Shu-Sheng Chou | en |
| dc.contributor.author | 周書聖 | zh_TW |
| dc.date.accessioned | 2021-06-17T09:07:38Z | - |
| dc.date.available | 2019-12-02 | |
| dc.date.copyright | 2019-12-02 | |
| dc.date.issued | 2019 | |
| dc.date.submitted | 2019-11-28 | |
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/74790 | - |
| dc.description.abstract | 本論文係利用丹麥技術大學團隊開發之自由軟體GPAW，改善用來分析金原子塊材的科恩–沈呂九方程之計算方法。對於一個由金原子所組成的塊材來說，第一原理計算所採用的密度泛函理論包括了兩個計算量相當大的方程，其一為科恩–沈呂九方程的非線性特徵值問題，其二則是哈特里電位勢的帕松方程計算。對於密度泛函方程的離散，在本研究中考慮非週期邊界條件並採用實空間網格的有限差分法。
除了在實空間網格上執行科恩–沈呂九方程的有限差分法外，本文的目標是改進在大尺寸情形下的特徵值方程的計算，進而保存適合的疊代法。由於非週期性邊界條件及材料中原子的不規則分佈，造成所涉及的矩陣方程具不對稱的性質。在此，本文將共軛梯度法逐步發展成雙共軛梯度法與廣義最小殘量法，並比較這兩個新方法的正確性與計算效率。 | zh_TW |
| dc.description.abstract | To this thesis, the open source code GPAW, which had been developing by DTU Physics, is used to analyze the gold bulk system via different numeric methods. Simulations based on first-principle density functional theory for gold atom involves solving two most computationally expensive equations, namely, the nonlinear eigenvalue problem for Kohn-Sham equation and the inhomogeneous calculation of Poisson equation for the indispensable Hartree potential. For the discretization of the density-functional equation, in this study, adopting finite difference mode could implement it in motion real-space grids for the considerations of a reliable treatment of non-periodic boundary conditions and for an efficient parallelization of the eigenvalue and Poisson equations that require most of the computing time.
Besides running the finite difference Kohn-Sham equation on real-space grids, aiming to improve the computation of large-sized eigenvalue equation saving the iterative solvers that are suitable implemented in parallel. Due to the asymmetric nature of the involved matrix equations owing to the non-periodic boundary conditions and the indefinite nature resulting from irregular distribution of atoms in the materials, this thesis develop the conjugate gradient method into biconjugate gradient method and generalized minimal residual method, and investigate for their performance between input materials. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-17T09:07:38Z (GMT). No. of bitstreams: 1 ntu-108-R05525107-1.pdf: 2799936 bytes, checksum: c30bbccedbe83ef26df61fedad7520af (MD5) Previous issue date: 2019 | en |
| dc.description.tableofcontents | 口試委員會審定書 #
誌謝 i 中文摘要 ii ABSTRACT iii 目錄 iv 圖目錄 vii 表目錄 ix 第一章 研究動機及目標 1 1.1 前言 1 1.2 模擬方法 1 1.3 文獻回顧 2 第二章 控制方程及其推導 3 2.1 第一原理計算方法 4 2.2 霍亨貝格–柯恩定理 4 2.3 柯恩–沈呂九控制方程 7 2.4 相關能泛函的簡介 8 2.4.1 局部密度近似 8 2.4.2 廣義梯度密度近似 9 第三章 對於GPAW的簡介 11 3.1 GPAW發展簡史及其功能 11 3.2 GPAW之CUDA版的發展 13 3.3 GPAW所採用的模擬方法 15 3.4 GPAW裡的特徵值解法器 15 3.4.1 共軛梯度法 16 3.4.2 雙共軛梯度法 18 3.4.3 廣義最小殘量法 20 第四章 金原子塊材在計算中的一些基本定理 23 4.1 晶體結構與倒晶格 25 4.2 布里淵區與布洛赫定理 26 4.3 能帶理論計算 28 第五章 定義問題與參數設定 29 5.1 以GPAW實現金原子塊材計算 29 5.1.1 特徵值解法器的正確性 31 5.1.2 倒晶格點的取法與『Gamma centered』 33 5.1.3 倒晶格點的飽和情形 34 5.2 計算四顆金原子所組成的單位晶胞 36 5.3 氫氣的原子化能計算 39 5.3.1 氫氣與氫原子的參數設置 40 5.3.2 廣義最小殘量法與雙共軛梯度法的計算結果 41 第六章 結果與討論 43 6.1 特徵值解法於週期性問題的比較 43 6.2 特徵值解法於非週期性問題的比較 44 第七章 結論 47 參考文獻 48 附錄A 中英詞彙對照表中英對照表 52 附錄B SCCS計算主機的環境設置資料 54 附錄C GPAW計算金原子塊材的設置簡介 55 附錄D GPAW計算金原子塊材的步驟與程式 56 附錄E GPAW計算四顆金原子塊材的程式 58 附錄F GPAW計算氫原子與氫氣分子的設置簡介 59 附錄G GPAW計算氫原子與氫氣分子的步驟與程式 60 | |
| dc.language.iso | zh-TW | |
| dc.title | 以GPAW全盤探討金原子塊材的數值方法及其特性 | zh_TW |
| dc.title | A Comprehensive Numerical Study of Gold Molecular by GPAW | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 108-1 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 李佳翰,郭錦龍 | |
| dc.subject.keyword | 密度泛函理論,科恩–沈呂九方程,數值方法,雙共軛梯度法,廣義最小殘量法,電子能帶圖,布里淵區,倒晶格點, | zh_TW |
| dc.subject.keyword | Density functional theory,Kohn-Shame equation,Numerical method,Biconjugate gradient method,Generalized minimal residual method,Electronic band structure,Brillouin zone,K-Point, | en |
| dc.relation.page | 61 | |
| dc.identifier.doi | 10.6342/NTU201904342 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2019-11-29 | |
| dc.contributor.author-college | 工學院 | zh_TW |
| dc.contributor.author-dept | 工程科學及海洋工程學研究所 | zh_TW |
| 顯示於系所單位： | 工程科學及海洋工程學系 | |
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