Self-consistent-field calculations using Chebyshev-filtered subspace iteration

Yunkai Zhou, Yousef Saad, Murilo L. Tiago, James R. Chelikowsky

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143 Scopus citations


The power of density functional theory is often limited by the high computational demand in solving an eigenvalue problem at each self-consistent-field (SCF) iteration. The method presented in this paper replaces the explicit eigenvalue calculations by an approximation of the wanted invariant subspace, obtained with the help of well-selected Chebyshev polynomial filters. In this approach, only the initial SCF iteration requires solving an eigenvalue problem, in order to provide a good initial subspace. In the remaining SCF iterations, no iterative eigensolvers are involved. Instead, Chebyshev polynomials are used to refine the subspace. The subspace iteration at each step is easily five to ten times faster than solving a corresponding eigenproblem by the most efficient eigen-algorithms. Moreover, the subspace iteration reaches self-consistency within roughly the same number of steps as an eigensolver-based approach. This results in a significantly faster SCF iteration.

Original languageEnglish (US)
Pages (from-to)172-184
Number of pages13
JournalJournal of Computational Physics
Issue number1
StatePublished - Nov 20 2006

Bibliographical note

Funding Information:
Work supported by DOE under Grants DE-FG02-03ER25585 and DE-FG02-03ER15491, by NSF Grants ITR-0551195 and ITR-0428774, and by the Minnesota Supercomputing Institute.


  • Chebyshev polynomial filter
  • Density functional theory
  • Eigenproblem
  • Real-space pseudopotential
  • Self-consistent-field
  • Subspace iteration


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