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Title: Linear Multigrid Techniques in Self-consistent Electronic Structure Calculations

Abstract

Ab initio DFT electronic structure calculations involve an iterative process to solve the Kohn-Sham equations for an Hamiltonian depending on the electronic density. We discretize these equations on a grid by finite differences. Trial eigenfunctions are improved at each step of the algorithm using multigrid techniques to efficiently reduce the error at all length scale, until self-consistency is achieved. In this paper we focus on an iterative eigensolver based on the idea of inexact inverse iteration, using multigrid as a preconditioner. We also discuss how this technique can be used for electrons described by general non-orthogonal wave functions, and how that leads to a linear scaling with the system size for the computational cost of the most expensive parts of the algorithm.

Authors:
Publication Date:
Research Org.:
Lawrence Livermore National Lab., CA (US)
Sponsoring Org.:
USDOE Office of Defense Programs (DP) (US)
OSTI Identifier:
791582
Report Number(s):
UCRL-JC-138186
TRN: US200304%%513
DOE Contract Number:  
W-7405-Eng-48
Resource Type:
Conference
Resource Relation:
Conference: NATO Advanced Research Workshop on Multiscale Computational Methods in Chemistry and Biology, Eilat (IL), 04/05/2000--04/07/2000; Other Information: PBD: 23 May 2000
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ALGORITHMS; BIOLOGY; CHEMISTRY; EIGENFUNCTIONS; ELECTRONIC STRUCTURE; ELECTRONS; HAMILTONIANS; NATO; WAVE FUNCTIONS

Citation Formats

Fattebert, J-L. Linear Multigrid Techniques in Self-consistent Electronic Structure Calculations. United States: N. p., 2000. Web.
Fattebert, J-L. Linear Multigrid Techniques in Self-consistent Electronic Structure Calculations. United States.
Fattebert, J-L. Tue . "Linear Multigrid Techniques in Self-consistent Electronic Structure Calculations". United States. https://www.osti.gov/servlets/purl/791582.
@article{osti_791582,
title = {Linear Multigrid Techniques in Self-consistent Electronic Structure Calculations},
author = {Fattebert, J-L},
abstractNote = {Ab initio DFT electronic structure calculations involve an iterative process to solve the Kohn-Sham equations for an Hamiltonian depending on the electronic density. We discretize these equations on a grid by finite differences. Trial eigenfunctions are improved at each step of the algorithm using multigrid techniques to efficiently reduce the error at all length scale, until self-consistency is achieved. In this paper we focus on an iterative eigensolver based on the idea of inexact inverse iteration, using multigrid as a preconditioner. We also discuss how this technique can be used for electrons described by general non-orthogonal wave functions, and how that leads to a linear scaling with the system size for the computational cost of the most expensive parts of the algorithm.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2000},
month = {5}
}

Conference:
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