Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 255, Issue -, Pages 16-30Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2013.07.020
Keywords
Hybrid preconditioning; Iterative diagonalization; Ill conditioned GHEP; Steepest descent method; Electronic structure calculation
Funding
- UC Lab Fees Research Program [118128]
- U.S. Department of Energy by Lawrence Livermore National Laboratory [DE-AC52-07NA27344]
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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. (c) 2013 Elsevier Inc. All rights reserved.
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