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Title: Hybrid preconditioning for iterative diagonalization of ill-conditioned generalized eigenvalue problems in electronic structure calculations

The iterative diagonalization of a sequence of large ill-conditioned generalized eigenvalue problems is a computational bottleneck in quantum mechanical methods employing a nonorthogonal basis for ab initio electronic structure calculations. We propose a hybrid preconditioning scheme to effectively combine global and locally accelerated preconditioners for rapid iterative diagonalization of such eigenvalue problems. In partition-of-unity finite-element (PUFE) pseudopotential density-functional calculations, employing a nonorthogonal basis, we show that the hybrid preconditioned block steepest descent method is a cost-effective eigensolver, outperforming current state-of-the-art global preconditioning schemes, and comparably efficient for the ill-conditioned generalized eigenvalue problems produced by PUFE as the locally optimal block preconditioned conjugate-gradient method for the well-conditioned standard eigenvalue problems produced by planewave methods.
Authors:
 [1] ;  [2] ;  [3] ;  [4] ;  [5]
  1. LMAM and School of Mathematical Sciences, Peking University, Beijing 100871 (China)
  2. (United States)
  3. Department of Computer Science and Department of Mathematics, University of California, Davis 95616 (United States)
  4. Condensed Matter and Materials Division, Lawrence Livermore National Laboratory, Livermore, CA 94550 (United States)
  5. Department of Civil and Environmental Engineering, University of California, Davis 95616 (United States)
Publication Date:
OSTI Identifier:
22230825
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 255; Other Information: Copyright (c) 2013 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:
97 MATHEMATICAL METHODS AND COMPUTING; 74 ATOMIC AND MOLECULAR PHYSICS; DENSITY FUNCTIONAL METHOD; EIGENVALUES; ELECTRONIC STRUCTURE; FINITE ELEMENT METHOD; ITERATIVE METHODS; QUANTUM MECHANICS