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

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.
Authors:
 [1] ;  [2] ;  [3]
  1. Department of Mathematics, Southern Methodist University, Dallas, TX 75275 (United States)
  2. Center for Computational Materials, Institute for Computational Engineering and Science, and Departments of Physics and Chemical Engineering, University of Texas, Austin, TX 78712 (United States)
  3. Department of Computer Science and Engineering, University of Minnesota, MN 55455 (United States)
Publication Date:
OSTI Identifier:
22382122
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 274; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
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