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On the “Preconditioning” Function Used in Planewave DFT Calculations and its Generalization

Part of: Basic linear algebra Numerical linear algebra General and miscellaneous specific topics Graph theory

Published online by Cambridge University Press:  03 July 2015

Yunkai Zhou ,
James R. Chelikowsky ,
Xingyu Gao  and
Aihui Zhou
Yunkai Zhou*
Affiliation:
Department of Mathematics, Southern Methodist University, Dallas, TX 75275, USA
James R. Chelikowsky
Affiliation:
Center for Computational Materials, Institute for Computational Engineering and Science, and Departments of Physics and Chemical Engineering, University of Texas, Austin, TX 78712, USA
Xingyu Gao
Affiliation:
HPCC, Institute of Applied Physics and Computational Mathematics, Beijing, 100094, China
Aihui Zhou
Affiliation:
LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
*
*Corresponding author. Email addresses: yzhou@smu.edu (Y. Zhou), jrc@ices.utexas.edu (J. R. Chelikowsky), gao_xingyu@iapcm.ac.cn (X. Gao), azhou@lsec.cc.ac.cn (A. Zhou)
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Abstract

The Teter, Payne, and Allan “preconditioning” function plays a significant role in planewave DFT calculations. This function is often called the TPA preconditioner. We present a detailed study of this “preconditioning” function. We develop a general formula that can readily generate a class of “preconditioning” functions. These functions have higher order approximation accuracy and fulfill the two essential “preconditioning” purposes as required in planewave DFT calculations. Our general class of functions are expected to have applications in other areas.

Keywords

Density functional theoryplanewavepreconditioning functioneigenvalue problem

MSC classification

Secondary: 00A69: General applied mathematics 05C50: Graphs and linear algebra (matrices, eigenvalues, etc.) 15A18: Eigenvalues, singular values, and eigenvectors 65F15: Eigenvalues, eigenvectors
Type
Research Article
Information
Communications in Computational Physics , Volume 18 , Issue 1 , July 2015 , pp. 167 - 179
Copyright
Copyright © Global-Science Press 2015 

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