Related papers: Basis Functions for Linear-Scaling First-Principle…
We reexamine the recently introduced basis-set correction theory based on density-functional theory consisting in correcting the basis-set incompleteness error of wave-function methods using a density functional. We use a one-dimensional…
This paper addresses a multi-scale finite element method for second order linear elliptic equations with arbitrarily rough coefficient. We propose a local oversampling method to construct basis functions that have optimal local…
We develop efficient and high-order accurate finite difference methods for elliptic partial differential equations in complex geometry in the Difference Potentials framework. The main novelty of the developed schemes is the use of local…
We present a method to discretize the Kohn-Sham Hamiltonian matrix in the pseudopotential framework by a small set of basis functions automatically contracted from a uniform basis set such as planewaves. Each basis function is localized…
We study the relaxations, surface energies, and work functions of low index metallic surfaces using pseudopotential plane-wave density-functional calculations within the generalized gradient approximation. We study here the (100), (110),…
Approximation/interpolation from spaces of positive definite or conditionally positive definite kernels is an increasingly popular tool for the analysis and synthesis of scattered data, and is central to many meshless methods. For a set of…
We develop a numerical approach based on the sinc basis set for first-principles electronic structure calculations in one-dimensional systems. The method exploits the inherent accuracy and non-local character of the sinc functions to handle…
There are many ways to numerically represent of chemical systems in order to compute their electronic structure. Basis functions may be localized in real-space (atomic orbitals), in momentum-space (plane waves), or in both components of…
A brief review of the SIESTA project is presented in the context of linear-scaling density-functional methods for electronic-structure calculations and molecular-dynamics simulations of systems with a large number of atoms. Applications of…
The spatial random-effects model is flexible in modeling spatial covariance functions, and is computationally efficient for spatial prediction via fixed rank kriging. However, the success of this model depends on an appropriate set of basis…
We discuss a method for determining the optimally-localized set of generalized Wannier functions associated with a set of Bloch bands in a crystalline solid. By ``generalized Wannier functions'' we mean a set of localized orthonormal…
Orbital-free density functional theory (OF-DFT) runs at low computational cost that scales linearly with the number of simulated atoms, making it suitable for large-scale material simulations. It is generally considered that OF-DFT strictly…
We present an approach to solid-state electronic-structure calculations based on the finite-element method. In this method, the basis functions are strictly local, piecewise polynomials. Because the basis is composed of polynomials, the…
An algorithm for first-principles electronic structure calculations having a computational cost which scales linearly with the system size is presented. Our method exploits the real-space localization of the density matrix, and in this…
We analyze in detail the error that arises from the linearization in linearized augmented-plane-wave (LAPW) basis functions around predetermined energies $E_l$ and show that it can lead to undesirable dependences of the calculated results…
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…
In this paper, we develop and analyze a rigorous multiscale upscaling method for dual continuum model, which serves as a powerful tool in subsurface formation applications. Our proposed method is capable of identifying different continua…
In the context of functional data analysis, probability density functions as non-negative functions are characterized by specific properties of scale invariance and relative scale which enable to represent them with the unit integral…
Density functional theory offers accurate structure prediction at acceptable computational cost, but commonly used approximations suffer from delocalization error; this results in inaccurate predictions of quantities such as energy band…
Locality of compact one-electron orbitals expanded strictly in terms of local subsets of basis functions can be exploited in density functional theory (DFT) to achieve linear growth of computation time with systems size, crucial in…