Multigrid method for electronic structure calculations

M. Heiskanen, M.J. Puska, R.M. Nieminen

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A general real-space multigrid algorithm for the self-consistent solution of the Kohn-Sham equations appearing in the state-of-the-art electronic-structure calculations is described. The most important part of the method is the multigrid solver for the Schrödinger equation. Our choice is the Rayleigh quotient multigrid method (RQMG), which applies directly to the minimization of the Rayleigh quotient on the finest level. Very coarse correction grids can be used, because there is, in principle, no need to represent the states on the coarse levels. The RQMG method is generalized for the simultaneous solution of all the states of the system using a penalty functional to keep the states orthogonal. The performance of the scheme is demonstrated by applying it in a few molecular and solid-state systems described by nonlocal norm-conserving pseudopotentials.
Original languageEnglish
Article number245106
Pages (from-to)1-8
Number of pages8
JournalPhysical Review B
Issue number24
Publication statusPublished - 1 Jun 2001
MoE publication typeA1 Journal article-refereed


  • density functional theory
  • electronic structure
  • multigrid

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