2,250 research outputs found
Compressed representation of Kohn-Sham orbitals via selected columns of the density matrix
Given a set of Kohn-Sham orbitals from an insulating system, we present a
simple, robust, efficient and highly parallelizable method to construct a set
of, optionally orthogonal, localized basis functions for the associated
subspace. Our method explicitly uses the fact that density matrices associated
with insulating systems decay exponentially along the off-diagonal direction in
the real space representation. Our method avoids the usage of an optimization
procedure, and the localized basis functions are constructed directly from a
set of selected columns of the density matrix (SCDM). Consequently, the only
adjustable parameter in our method is the truncation threshold of the localized
basis functions. Our method can be used in any electronic structure software
package with an arbitrary basis set. We demonstrate the numerical accuracy and
parallel scalability of the SCDM procedure using orbitals generated by the
Quantum ESPRESSO software package. We also demonstrate a procedure for
combining SCDM with Hockney's algorithm to efficiently perform Hartree-Fock
exchange energy calculations with near linear scaling.Comment: 7 pages, 4 figures; short example code for computing the SCDM;
parallel scaling results; slightly restructured introduction and
clarification of the input needed to compute the SCD
SCDM-k: Localized orbitals for solids via selected columns of the density matrix
The recently developed selected columns of the density matrix (SCDM) method
[J. Chem. Theory Comput. 11, 1463, 2015] is a simple, robust, efficient and
highly parallelizable method for constructing localized orbitals from a set of
delocalized Kohn-Sham orbitals for insulators and semiconductors with
point sampling of the Brillouin zone. In this work we generalize the SCDM
method to Kohn-Sham density functional theory calculations with k-point
sampling of the Brillouin zone, which is needed for more general electronic
structure calculations for solids. We demonstrate that our new method, called
SCDM-k, is by construction gauge independent and is a natural way to describe
localized orbitals. SCDM-k computes localized orbitals without the use of an
optimization procedure, and thus does not suffer from the possibility of being
trapped in a local minimum. Furthermore, the computational complexity of using
SCDM-k to construct orthogonal and localized orbitals scales as O(N log N )
where N is the total number of k-points in the Brillouin zone. SCDM-k is
therefore efficient even when a large number of k-points are used for Brillouin
zone sampling. We demonstrate the numerical performance of SCDM-k using systems
with model potentials in two and three dimensions.Comment: 25 pages, 7 figures; added more background sections, clarified
presentation of the algorithm, revised the presentation of previous work,
added a more high level overview of the new algorithm, and mildly clarified
the presentation of the results (there were no changes to the numerical
results themselves
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
Computational Physics on Graphics Processing Units
The use of graphics processing units for scientific computations is an
emerging strategy that can significantly speed up various different algorithms.
In this review, we discuss advances made in the field of computational physics,
focusing on classical molecular dynamics, and on quantum simulations for
electronic structure calculations using the density functional theory, wave
function techniques, and quantum field theory.Comment: Proceedings of the 11th International Conference, PARA 2012,
Helsinki, Finland, June 10-13, 201
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