Iterative Procedures for Nonlinear Integral Equations
Journal of the ACM (JACM)
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
SIAM Journal on Scientific Computing
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
A Reduced-Basis Element Method
Journal of Scientific Computing
Discontinuous Galerkin method based on non-polynomial approximation spaces
Journal of Computational Physics
Finite element approach for density functional theory calculations on locally-refined meshes
Journal of Computational Physics
Certified Reduced Basis Methods and Output Bounds for the Harmonic Maxwell's Equations
SIAM Journal on Scientific Computing
SelInv---An Algorithm for Selected Inversion of a Sparse Symmetric Matrix
ACM Transactions on Mathematical Software (TOMS)
SIAM Journal on Scientific Computing
Optimized local basis set for Kohn-Sham density functional theory
Journal of Computational Physics
Discontinuous Galerkin Methods: Theory, Computation and Applications
Discontinuous Galerkin Methods: Theory, Computation and Applications
Optimized local basis set for Kohn-Sham density functional theory
Journal of Computational Physics
An h-adaptive finite element solver for the calculations of the electronic structures
Journal of Computational Physics
Hi-index | 31.46 |
Kohn-Sham density functional theory is one of the most widely used electronic structure theories. In the pseudopotential framework, uniform discretization of the Kohn-Sham Hamiltonian generally results in a large number of basis functions per atom in order to resolve the rapid oscillations of the Kohn-Sham orbitals around the nuclei. Previous attempts to reduce the number of basis functions per atom include the usage of atomic orbitals and similar objects, but the atomic orbitals generally require fine tuning in order to reach high accuracy. We present 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. The resulting basis functions are localized in the real space, and are discontinuous in the global domain. The continuous Kohn-Sham orbitals and the electron density are evaluated from the discontinuous basis functions using the discontinuous Galerkin (DG) framework. Our method is implemented in parallel and the current implementation is able to handle systems with at least thousands of atoms. Numerical examples indicate that our method can reach very high accuracy (less than 1meV) with a very small number (4-40) of basis functions per atom.