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

  • Yunkai Zhou (a1), James R. Chelikowsky (a2), Xingyu Gao (a3) and Aihui Zhou (a4)
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.

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Corresponding author
*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)
References
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[1]Banerjee, A. S., Elliott, R. S., and James, R. D.. A spectral scheme for Kohn-Sham density functional theory of clusters. ArXiv e-prints, arXiv:1404.3773, 2014.
[2]Benzi, M.. Preconditioning techniques for large linear systems: A survey. J. Comput. Phys., 182(2):418477, 2002.
[3]Engel, B. and Dreizler, R.M.. Density Functional Theory: An Advanced Course. Theoretical and Mathematical Physics. Springer, 2011.
[4]Giannozzi, P.et al.. QUANTUM ESPRESSO: A modular and open-source software project for quantum simulations of materials. Journal of Physics: Condensed Matter, 21(39):395502 (19pp), 2009.
[5]Gonze, X.et al.. ABINIT: First-principles approach of materials and nanosystem properties. Computer Phys. Commun., 180:25822615, 2009.
[6]Hohenberg, P. and Kohn, W.. Inhomogeneous electron gas. Phys. Rev., 136:B864871, 1964.
[7]Kaxiras, E.. Atomic and Electronic Structure of Solids. Cambridge University Press, 2003.
[8]Kohanoff, J.. Electronic Structure Calculations for Solids and Molecules: Theory and Computational Methods. Cambridge Univ. Press, 2006.
[9]Kohn, W. and Sham, L. J.. Self-consistent equations including exchange and correlation effects. Phys. Rev., 140:A11331138, 1965.
[10]Kresse, G. and Furthmü ller, J.. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B, 54(16):1116911186, 1996.
[11]Levitt, A. and Torrent, M.. Parallel eigensolvers in plane-wave density functional theory. Comp. Phys. Comm., 187:98105, 2015.
[12]Martin, R. M.. Electronic Structure: Basic Theory and Practical Methods. Cambridge University Press, 2004.
[13]Motamarri, P. and Gavini, V.. A subquadratic-scaling subspace projection method for large-scale Kohn-Sham density functional theory calculations using spectral finite-element discretization. ArXiv e-prints, arXiv:1406.2600, 2014.
[14]Saad, Y.. Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, second edition, 2003.
[15]Sholl, D. and Steckel, J. A.. Density Functional Theory: A Practical Introduction. Wiley-Interscience, 2009.
[16]Teter, M. P., Payne, M. C., and Allan, D. C.. Solution of Schrödinger’s equation for large systems. Phys. Rev. B, 40:1225512263, 1989.
[17]ABINIT webpage. http://www.abinit.org/.
[18]Quantum ESPRESSO webpage. http://www.quantum-espresso.org/.
[20]Wilkinson, J. H.. The Algebraic Eigenvalue Problem. Oxford University Press, 1965.
[21]Yang, C., Meza, J. C., Lee, B., and Wang, L.-W.. KSSOLV — a MATLAB Toolbox for Solving the Kohn-Sham Equations. ACM Trans. Math. Softw., 36(2):10:135, 2009.
[22]Zhou, Y.. A block Chebyshev-Davidson method with inner-outer restart for large eigenvalue problems. J. Comput. Phys., 229(24):91889200, 2010.
[23]Zhou, Y. and Li, R.-C.. On the essence of “pre-conditioned” eigen-algorithms. (to be submitted).
[24]Zhou, Y. and Saad, Y.. A Chebyshev-Davidson algorithm for large symmetric eigenvalue problems. SIAM J. Matrix Anal. Appl., 29(3):954971, 2007.
[25]Zhou, Y., Saad, Y., Tiago, M. L., and Chelikowsky, J. R.. Parallel self-consistent-field calculations using Chebyshev-filtered subspace acceleration. Phys. Rev. E, 74(6):066704, 2006.
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Communications in Computational Physics
  • ISSN: 1815-2406
  • EISSN: 1991-7120
  • URL: /core/journals/communications-in-computational-physics
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