1,320 research outputs found
ELSI: A Unified Software Interface for Kohn-Sham Electronic Structure Solvers
Solving the electronic structure from a generalized or standard eigenproblem
is often the bottleneck in large scale calculations based on Kohn-Sham
density-functional theory. This problem must be addressed by essentially all
current electronic structure codes, based on similar matrix expressions, and by
high-performance computation. We here present a unified software interface,
ELSI, to access different strategies that address the Kohn-Sham eigenvalue
problem. Currently supported algorithms include the dense generalized
eigensolver library ELPA, the orbital minimization method implemented in
libOMM, and the pole expansion and selected inversion (PEXSI) approach with
lower computational complexity for semilocal density functionals. The ELSI
interface aims to simplify the implementation and optimal use of the different
strategies, by offering (a) a unified software framework designed for the
electronic structure solvers in Kohn-Sham density-functional theory; (b)
reasonable default parameters for a chosen solver; (c) automatic conversion
between input and internal working matrix formats, and in the future (d)
recommendation of the optimal solver depending on the specific problem.
Comparative benchmarks are shown for system sizes up to 11,520 atoms (172,800
basis functions) on distributed memory supercomputing architectures.Comment: 55 pages, 14 figures, 2 table
A robust and efficient implementation of LOBPCG
Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) is widely
used to compute eigenvalues of large sparse symmetric matrices. The algorithm
can suffer from numerical instability if it is not implemented with care. This
is especially problematic when the number of eigenpairs to be computed is
relatively large. In this paper we propose an improved basis selection strategy
based on earlier work by Hetmaniuk and Lehoucq as well as a robust convergence
criterion which is backward stable to enhance the robustness. We also suggest
several algorithmic optimizations that improve performance of practical LOBPCG
implementations. Numerical examples confirm that our approach consistently and
significantly outperforms previous competing approaches in both stability and
speed
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