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

Published online by Cambridge University Press:  03 July 2015

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: [email protected] (Y. Zhou), [email protected] (J. R. Chelikowsky), [email protected] (X. Gao), [email protected] (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.

Type
Research Article
Copyright
Copyright © Global-Science Press 2015 

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