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The discretization of the double-layer potential integral equation for the interior Dirichlet Laplace problem in a domain with smooth boundary results in a linear system that has a bounded condition number. Thus, the number of iterations…
The current generation of covariant mean-field models has had many successes in calculations of bulk observables for medium to heavy nuclei, but there remain many open questions. New challenges are confronted when trying to systematically…
Reduced density-matrix functional theory (RDMFT) provides a variational route to electronic correlations beyond conventional density-functional approximations, but explicit evaluations of density-matrix functionals still scale exponentially…
The augmented Lagrangiam method (ALM), widely used in quantum chemistry constrained optimization problems, is applied in the context of the nuclear Density Functional Theory (DFT) in the self-consistent constrained Skyrme…
This article is part-I of a review of density-functional theory (DFT) that is the most widely used method for calculating electronic structure of materials. The accuracy and ease of numerical implementation of DFT methods has resulted in…
We present a computational approach which is tailored for reducing the complexity of the description of extended systems at the density functional theory level. We define a recipe for generating a set of localized basis functions which are…
We consider the numerical approximation of the radiative transfer equation using discontinuous angular and continuous spatial approximations for the even parts of the solution. The even-parity equations are solved using a diffusion…
In this paper, we investigate the energy minimization model of the ensemble Kohn-Sham density functional theory for metallic systems, in which a pseudo-eigenvalue matrix and a general smearing approach are involved. We study the invariance…
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…
We show that a lattice formulation of density-functional theory (DFT), guided by renormalization-group concepts, can be used to obtain numerical predictions of energy gaps, spin-density profiles, critical exponents, sound velocities,…
In this paper, we study a few theoretical issues in the discretized Kohn-Sham (KS) density functional theory (DFT). The equivalence between either a local or global minimizer of the KS total energy minimization problem and the solution to…
PDE-constrained optimization problems have been barely solved by radial basis functions (RBFs) methods [Pearson, 2013]. It is well known that RBF methods can attain an exponential rate of convergence when $C^{\infty}$ kernels are used,…
We have developed and implemented a new quantum molecular dynamics approximation that allows fast and accurate simulations of dense plasmas from cold to hot conditions. The method is based on a carefully designed orbital-free implementation…
We present a computationally efficient approach to perform large-scale all-electron density functional theory calculations by enriching the classical finite element basis with compactly supported atom-centered numerical basis functions that…
An approximate solution to the time-dependent density functional theory (TDDFT) response equations for finite systems is developed, yielding corrections to the single-pole approximation. These explain why allowed Kohn-Sham transition…
The general procedure underlying Hartree-Fock and Kohn-Sham density functional theory calculations consists in optimizing orbitals for a self-consistent solution of the Roothaan-Hall equations in an iterative process. It is often ignored…
A method is presented, which employs the density matrix renormalization group technique in order to construct exact ground state exchange correlation functionals for models of correlated electron systems coupled to external reservoirs. The…
Discrete diffusion models have emerged as powerful tools for high-quality data generation. Despite their success in discrete spaces, such as text generation tasks, the acceleration of discrete diffusion models remains under-explored. In…
Recent advances in fast sampling methods for diffusion models have demonstrated significant potential to accelerate generation on image modalities. We apply these methods to 3-dimensional molecular conformations by building on the recently…
Reliable and robust convergence to the electronic ground state within density functional theory (DFT) Kohn-Sham (KS) calculations remains a thorny issue in many systems of interest. In such cases, charge sloshing can delay or completely…