Chebyshev-filtered subspace iteration method free of sparse diagonalization for solving the Kohn–Sham equation

Journal Article · Wed Oct 01 04:00:00 EDT 2014 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2014.06.056· OSTI ID:22382122

Zhou, Yunkai ^[1]; Saad, Yousef ^[2]

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1. Department of Mathematics, Southern Methodist University, Dallas, TX 75275 (United States)
2. Department of Computer Science and Engineering, University of Minnesota, MN 55455 (United States)

First-principles density functional theory (DFT) calculations for the electronic structure problem require a solution of the Kohn–Sham equation, which requires one to solve a nonlinear eigenvalue problem. Solving the eigenvalue problem is usually the most expensive part in DFT calculations. Sparse iterative diagonalization methods that compute explicit eigenvectors can quickly become prohibitive for large scale problems. The Chebyshev-filtered subspace iteration (CheFSI) method avoids most of the explicit computation of eigenvectors and results in a significant speedup over iterative diagonalization methods for the DFT self-consistent field (SCF) calculations. However, the original formulation of the CheFSI method utilizes a sparse iterative diagonalization at the first SCF step to provide initial vectors for subspace filtering at latter SCF steps. This diagonalization is expensive for large scale problems. We develop a new initial filtering step to avoid completely this diagonalization, thus making the CheFSI method free of sparse iterative diagonalizations at all SCF steps. Our new approach saves memory usage and can be two to three times faster than the original CheFSI method.

• OSTI ID: 22382122
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 274; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DENSITY FUNCTIONAL METHOD
DIFFERENTIAL EQUATIONS
EIGENVALUES
EIGENVECTORS
ELECTRONIC STRUCTURE
FILTERS
HAMILTONIANS
ITERATIVE METHODS
MATHEMATICAL SOLUTIONS
NONLINEAR PROBLEMS
POTENTIALS
SELF-CONSISTENT FIELD
SPACE
VECTORS