Numerical approximations of a nonlinear eigenvalue problem and applications to a density functional model

被引：27
作者：
Chen, Huajie [1 ,2 ]
Gong, Xingao [3 ]
Zhou, Aihui [1 ]
机构：
[1] Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China
[2] Chinese Acad Sci, Grad Univ, Beijing 100190, Peoples R China
[3] Fudan Univ, Dept Phys, Shanghai 200433, Peoples R China
来源：
MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2010年 / 33卷 / 14期
基金：
美国国家科学基金会;
关键词：
eigenvalue; Galerkin discretization; nonlinear; numerical approximation; density functional; orbital-free; GROUND-STATE SOLUTION; FINITE-DIMENSIONAL APPROXIMATIONS; REAL-SPACE METHOD; THOMAS-FERMI; MOLECULAR-DYNAMICS; TOTAL-ENERGY; CONVERGENCE; ATOMS; ALGORITHMS;
D O I：
10.1002/mma.1292
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study numerical approximations of a nonlinear eigenvalue problem and consider applications to a density functional model. We prove the convergence of numerical approximations. In particular, we establish several upper bounds of approximation errors and report some numerical results of finite element electronic structure calculations that support our theory. Copyright (C) 2010 John Wiley & Sons, Ltd.
引用
收藏
页码：1723 / 1742
页数：20
相关论文
共 56 条
[1]  
Adams R., 1985, Sobolev Spaces
[2]   Numerical solution of the two-dimensional Gross-Pitaevskii equation for trapped interacting atoms [J].
Adhikari, SK .
PHYSICS LETTERS A, 2000, 265 (1-2) :91-96
[3]  
Agmon S., 1981, LECT EXPONENTIAL DEC
[4]  
[Anonymous], 2007, SPECTRAL METHODS
[5]   FINITE ELEMENT-GALERKIN APPROXIMATION OF THE EIGENVALUES AND EIGENVECTORS OF SELFADJOINT PROBLEMS [J].
BABUSKA, I ;
OSBORN, JE .
MATHEMATICS OF COMPUTATION, 1989, 52 (186) :275-297
[6]  
Babuska I., 1991, HDB NUMERICAL ANAL, V2
[7]   Computing the ground state solution of Bose-Einstein condensates by a normalized gradient flow [J].
Bao, WZ ;
Du, Q .
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2004, 25 (05) :1674-1697
[8]   Ground-state solution of Bose-Einstein condensate by directly minimizing the energy functional [J].
Bao, WZ ;
Tang, WJ .
JOURNAL OF COMPUTATIONAL PHYSICS, 2003, 187 (01) :230-254
[9]   Real-space mesh techniques in density-functional theory [J].
Beck, TL .
REVIEWS OF MODERN PHYSICS, 2000, 72 (04) :1041-1080
[10]   THE THOMAS-FERMI-VONWEIZSACKER THEORY OF ATOMS AND MOLECULES [J].
BENGURIA, R ;
BREZIS, H ;
LIEB, EH .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1981, 79 (02) :167-180
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