Chebyshev polynomial filtered subspace iteration in the discontinuous Galerkin method for large-scale electronic structure calculations.

@article{Banerjee2016ChebyshevPF,
  title={Chebyshev polynomial filtered subspace iteration in the discontinuous Galerkin method for large-scale electronic structure calculations.},
  author={Amartya S Banerjee and Lin Lin and Wei Hu and Chao Yang and John E. Pask},
  journal={The Journal of chemical physics},
  year={2016},
  volume={145 15},
  pages={
          154101
        }
}
The Discontinuous Galerkin (DG) electronic structure method employs an adaptive local basis (ALB) set to solve the Kohn-Sham equations of density functional theory 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… Expand
Two-Level Chebyshev Filter Based Complementary Subspace Method: Pushing the Envelope of Large-Scale Electronic Structure Calculations.
TLDR
A novel iterative strategy for Kohn-Sham density functional theory calculations aimed at large systems, applicable to metals and insulators alike, that reduces the cost of large metallic calculations significantly, while eliminating subspace diagonalization for insulating systems altogether. Expand
Discontinuous Galerkin discretization for quantum simulation of chemistry
Methods for electronic structure based on Gaussian and molecular orbital discretizations offer a well established, compact representation that forms much of the foundation of correlated quantumExpand
Adaptive local basis set for Kohn-Sham density functional theory in a discontinuous Galerkin framework II: Force, vibration, and molecular dynamics calculations
TLDR
It is demonstrated that, under mild assumptions, the computation of atomic forces can scale nearly linearly with the number of atoms in the system using the adaptive local basis set, and the Hellmann-Feynman force is sufficient for basis sizes of a few tens of basis functions per atom. Expand
Orbital-enriched flat-top partition of unity method for the Schrödinger eigenproblem
Abstract Quantum mechanical calculations require the repeated solution of a Schrodinger equation for the wavefunctions of the system, from which materials properties follow. Recent work has shown theExpand
Interpolative Separable Density Fitting Decomposition for Accelerating Hybrid Density Functional Calculations with Applications to Defects in Silicon.
TLDR
The ACE-ISDF method is used to geometrically optimize a 1000-atom silicon system with a vacancy defect using the HSE06 functional and computes its electronic structure, finding that that the computed energy gap is much closer to the experimental value compared to that produced by semilocal functionals in the DFT calculations. Expand
Discrete discontinuous basis projection method for large-scale electronic structure calculations.
TLDR
In calculations on a range of systems, it is found that accurate energies and forces are obtained with 8-25 basis functions per atom, reducing the dimension of the associated real-space eigenproblems by 1-3 orders of magnitude. Expand
Projected Commutator DIIS Method for Accelerating Hybrid Functional Electronic Structure Calculations.
TLDR
A new method is developed that enables the C-DIIS method to be efficiently employed in electronic structure calculations with a large basis set such as planewaves for the first time and it is demonstrated that in the context of ab initio molecular dynamics simulation with hybrid functionals one can extrapolate the gauge-fixing matrix to achieve the goal of extrapolating the entire density matrix implicitly along the MD trajectory. Expand
Globally Constructed Adaptive Local Basis Set for Spectral Projectors of Second Order Differential Operators
TLDR
A method to construct a basis set that is adaptive to the given differential operator, and the local features of the projector is built into the basis set using the discontinuous Galerkin (DG) method is developed. Expand
Chebyshev polynomial method to Landauer–Büttiker formula of quantum transport in nanostructures
Landauer-Buttiker formula describes the electronic quantum transports in nanostructures and molecules. It will be numerically demanding for simulations of complex or large size systems due to, forExpand
GLOBALLY CONSTRUCTED ADAPTIVE LOCAL BASIS SET FOR SPECTRAL PROJECTORS OF SECOND ORDER DIFFERENTIAL OPERATORS\ast
Spectral projectors of second order differential operators play an important role in quantum physics and other scientific and engineering applications. In order to resolve local features and toExpand
...
1
2
3
...

References

SHOWING 1-10 OF 67 REFERENCES
DGDFT: A massively parallel method for large scale density functional theory calculations.
TLDR
DGDFT can achieve 80% parallel efficiency on 128,000 high performance computing cores when it is used to study the electronic structure of 2D phosphorene systems with 3500-14 000 atoms, and results from a two-level parallelization scheme that will be described in detail. Expand
Chebyshev-filtered subspace iteration method free of sparse diagonalization for solving the Kohn-Sham equation
TLDR
A new initial filtering step is developed to avoid completely this diagonalization at the first SCF step, thus making the CheFSI method free of sparse iterative diagonalizations at all SCF steps, which saves memory usage and can be two to three times faster than the original Che FSI method. Expand
Parallel self-consistent-field calculations via Chebyshev-filtered subspace acceleration.
TLDR
An approach for implementing a nonlinear Chebyshev-filtered subspace iteration method, which avoids computing explicit eigenvectors except at the first self-consistent-field (SCF) iteration, and results in a significant speedup over methods based on standard diagonalization. Expand
Adaptive local basis set for Kohn-Sham density functional theory in a discontinuous Galerkin framework I: Total energy calculation
TLDR
This work presents a novel discretization scheme that adaptively and systematically builds the rapid oscillations of the Kohn-Sham orbitals around the nuclei as well as environmental effects into the basis functions. Expand
A spectral scheme for Kohn-Sham density functional theory of clusters
TLDR
A spectral method designed towards solving the Kohn-Sham equations for clusters, which allows for efficient calculation of the electronic structure of clusters with high accuracy and systematic convergence properties without the need for any artificial periodicity. Expand
Higher-order adaptive finite-element methods for Kohn-Sham density functional theory
TLDR
An a priori mesh-adaption technique is developed to construct a close to optimal finite-element discretization of Kohn-Sham density-functional theory (DFT), and it is suggested that the hexic spectral-element may be an optimal choice for the finite- element discretizations of the Kohn -Sham DFT problem. Expand
A posteriori error estimates for discontinuous Galerkin methods using non-polynomial basis functions. Part II: Eigenvalue problems
We present the first systematic work for deriving a posteriori error estimates for general non-polynomial basis functions in an interior penalty discontinuous Galerkin (DG) formulation for solvingExpand
Adaptive local basis set for Kohn-Sham density functional theory in a discontinuous Galerkin framework II: Force, vibration, and molecular dynamics calculations
TLDR
It is demonstrated that, under mild assumptions, the computation of atomic forces can scale nearly linearly with the number of atoms in the system using the adaptive local basis set, and the Hellmann-Feynman force is sufficient for basis sizes of a few tens of basis functions per atom. Expand
Self-consistent-field calculations using Chebyshev-filtered subspace iteration
TLDR
The method presented in this paper replaces the explicit eigenvalue calculations by an approximation of the wanted invariant subspace, obtained with the help of well-selected Chebyshev polynomial filters, which results in a significantly faster SCF iteration. Expand
Non-periodic finite-element formulation of Kohn–Sham density functional theory
We present a real-space, non-periodic, finite-element formulation for Kohn–Sham density functional theory (KS-DFT). We transform the original variational problem into a local saddle-point problem,Expand
...
1
2
3
4
5
...