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Title: Efficient preconditioning of the electronic structure problem in large scale ab initio molecular dynamics simulations

We present an improved preconditioning scheme for electronic structure calculations based on the orbital transformation method. First, a preconditioner is developed which includes information from the full Kohn-Sham matrix but avoids computationally demanding diagonalisation steps in its construction. This reduces the computational cost of its construction, eliminating a bottleneck in large scale simulations, while maintaining rapid convergence. In addition, a modified form of Hotelling’s iterative inversion is introduced to replace the exact inversion of the preconditioner matrix. This method is highly effective during molecular dynamics (MD), as the solution obtained in earlier MD steps is a suitable initial guess. Filtering small elements during sparse matrix multiplication leads to linear scaling inversion, while retaining robustness, already for relatively small systems. For system sizes ranging from a few hundred to a few thousand atoms, which are typical for many practical applications, the improvements to the algorithm lead to a 2-5 fold speedup per MD step.
Authors:
;  [1]
  1. Nanoscale Simulations, Department of Materials, ETH Zürich, Wolfgang-Pauli-Str. 27, CH-8093 Zürich (Switzerland)
Publication Date:
OSTI Identifier:
22490835
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 24; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; 97 MATHEMATICAL METHODS AND COMPUTING; ALGORITHMS; ATOMS; CONVERGENCE; ELECTRONIC STRUCTURE; ITERATIVE METHODS; MATHEMATICAL SOLUTIONS; MATRICES; MOLECULAR DYNAMICS METHOD; SIMULATION