1,142 research outputs found
Two-level Chebyshev filter based complementary subspace method: pushing the envelope of large-scale electronic structure calculations
We describe a novel iterative strategy for Kohn-Sham density functional
theory calculations aimed at large systems (> 1000 electrons), applicable to
metals and insulators alike. In lieu of explicit diagonalization of the
Kohn-Sham Hamiltonian on every self-consistent field (SCF) iteration, we employ
a two-level Chebyshev polynomial filter based complementary subspace strategy
to: 1) compute a set of vectors that span the occupied subspace of the
Hamiltonian; 2) reduce subspace diagonalization to just partially occupied
states; and 3) obtain those states in an efficient, scalable manner via an
inner Chebyshev-filter iteration. By reducing the necessary computation to just
partially occupied states, and obtaining these through an inner Chebyshev
iteration, our approach reduces the cost of large metallic calculations
significantly, while eliminating subspace diagonalization for insulating
systems altogether. We describe the implementation of the method within the
framework of the Discontinuous Galerkin (DG) electronic structure method and
show that this results in a computational scheme that can effectively tackle
bulk and nano systems containing tens of thousands of electrons, with chemical
accuracy, within a few minutes or less of wall clock time per SCF iteration on
large-scale computing platforms. We anticipate that our method will be
instrumental in pushing the envelope of large-scale ab initio molecular
dynamics. As a demonstration of this, we simulate a bulk silicon system
containing 8,000 atoms at finite temperature, and obtain an average SCF step
wall time of 51 seconds on 34,560 processors; thus allowing us to carry out 1.0
ps of ab initio molecular dynamics in approximately 28 hours (of wall time).Comment: Resubmitted version (version 2
Parallel Self-Consistent-Field Calculations via Chebyshev-Filtered Subspace Acceleration
Solving the Kohn-Sham eigenvalue problem constitutes the most computationally
expensive part in self-consistent density functional theory (DFT) calculations.
In a previous paper, we have proposed a nonlinear Chebyshev-filtered subspace
iteration method, which avoids computing explicit eigenvectors except at the
first SCF iteration. The method may be viewed as an approach to solve the
original nonlinear Kohn-Sham equation by a nonlinear subspace iteration
technique, without emphasizing the intermediate linearized Kohn-Sham eigenvalue
problem. It reaches self-consistency within a similar number of SCF iterations
as eigensolver-based approaches. However, replacing the standard
diagonalization at each SCF iteration by a Chebyshev subspace filtering step
results in a significant speedup over methods based on standard
diagonalization. Here, we discuss an approach for implementing this method in
multi-processor, parallel environment. Numerical results are presented to show
that the method enables to perform a class of highly challenging DFT
calculations that were not feasible before
Chebyshev polynomial filtered subspace iteration in the Discontinuous Galerkin method for large-scale electronic structure calculations
The Discontinuous Galerkin (DG) electronic structure method employs an
adaptive local basis (ALB) set to solve the Kohn-Sham equations of density
functional theory (DFT) in a discontinuous Galerkin framework. The adaptive
local basis is generated on-the-fly to capture the local material physics, and
can systematically attain chemical accuracy with only a few tens of degrees of
freedom per atom. A central issue for large-scale calculations, however, is the
computation of the electron density (and subsequently, ground state properties)
from the discretized Hamiltonian in an efficient and scalable manner. We show
in this work how Chebyshev polynomial filtered subspace iteration (CheFSI) can
be used to address this issue and push the envelope in large-scale materials
simulations in a discontinuous Galerkin framework. We describe how the subspace
filtering steps can be performed in an efficient and scalable manner using a
two-dimensional parallelization scheme, thanks to the orthogonality of the DG
basis set and block-sparse structure of the DG Hamiltonian matrix. The
on-the-fly nature of the ALBs requires additional care in carrying out the
subspace iterations. We demonstrate the parallel scalability of the DG-CheFSI
approach in calculations of large-scale two-dimensional graphene sheets and
bulk three-dimensional lithium-ion electrolyte systems. Employing 55,296
computational cores, the time per self-consistent field iteration for a sample
of the bulk 3D electrolyte containing 8,586 atoms is 90 seconds, and the time
for a graphene sheet containing 11,520 atoms is 75 seconds.Comment: Submitted to The Journal of Chemical Physic
O(N) methods in electronic structure calculations
Linear scaling methods, or O(N) methods, have computational and memory
requirements which scale linearly with the number of atoms in the system, N, in
contrast to standard approaches which scale with the cube of the number of
atoms. These methods, which rely on the short-ranged nature of electronic
structure, will allow accurate, ab initio simulations of systems of
unprecedented size. The theory behind the locality of electronic structure is
described and related to physical properties of systems to be modelled, along
with a survey of recent developments in real-space methods which are important
for efficient use of high performance computers. The linear scaling methods
proposed to date can be divided into seven different areas, and the
applicability, efficiency and advantages of the methods proposed in these areas
is then discussed. The applications of linear scaling methods, as well as the
implementations available as computer programs, are considered. Finally, the
prospects for and the challenges facing linear scaling methods are discussed.Comment: 85 pages, 15 figures, 488 references. Resubmitted to Rep. Prog. Phys
(small changes
Roadmap on Electronic Structure Codes in the Exascale Era
Electronic structure calculations have been instrumental in providing many
important insights into a range of physical and chemical properties of various
molecular and solid-state systems. Their importance to various fields,
including materials science, chemical sciences, computational chemistry and
device physics, is underscored by the large fraction of available public
supercomputing resources devoted to these calculations. As we enter the
exascale era, exciting new opportunities to increase simulation numbers, sizes,
and accuracies present themselves. In order to realize these promises, the
community of electronic structure software developers will however first have
to tackle a number of challenges pertaining to the efficient use of new
architectures that will rely heavily on massive parallelism and hardware
accelerators. This roadmap provides a broad overview of the state-of-the-art in
electronic structure calculations and of the various new directions being
pursued by the community. It covers 14 electronic structure codes, presenting
their current status, their development priorities over the next five years,
and their plans towards tackling the challenges and leveraging the
opportunities presented by the advent of exascale computing.Comment: Submitted as a roadmap article to Modelling and Simulation in
Materials Science and Engineering; Address any correspondence to Vikram
Gavini ([email protected]) and Danny Perez ([email protected]
Roadmap on Electronic Structure Codes in the Exascale Era
Electronic structure calculations have been instrumental in providing many important insights into a range of physical and chemical properties of various molecular and solid-state systems. Their importance to various fields, including materials science, chemical sciences, computational chemistry and device physics, is underscored by the large fraction of available public supercomputing resources devoted to these calculations. As we enter the exascale era, exciting new opportunities to increase simulation numbers, sizes, and accuracies present themselves. In order to realize these promises, the community of electronic structure software developers will however first have to tackle a number of challenges pertaining to the efficient use of new architectures that will rely heavily on massive parallelism and hardware accelerators. This roadmap provides a broad overview of the state-of-the-art in electronic structure calculations and of the various new directions being pursued by the community. It covers 14 electronic structure codes, presenting their current status, their development priorities over the next five years, and their plans towards tackling the challenges and leveraging the opportunities presented by the advent of exascale computing
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