Related papers: Multilevel domain decomposition for electronic str…

In this paper, we propose and analyze an additive domain decomposition method (DDM) for solving the high-frequency Helmholtz equation with the Sommerfeld radiation condition. In the proposed method, the computational domain is partitioned…

Linear scaling density functional theory approaches to electronic structure are often based on the tendency of electrons to localize even in large atomic and molecular systems. However, in many cases of actual interest, for example in…

Density functional theory (DFT) can run into serious difficulties with localized states in elements such as transition metals with occupied-d states and oxygen. In contrast, Hartree-Fock (HF) method can be a better approach for such…

The reduction of computational costs in the numerical solution of nonstationary problems is achieved through splitting schemes. In this case, solving a set of less computationally complex problems provides the transition to a new level in…

The dynamical mean field theory (DMFT) has become a standard technique for the study of strongly correlated models and materials overcoming some of the limitations of density functional approaches based on local approximations. An important…

A rigorous mathematical framework is provided for a substructuring-based domain-decomposition approach for nonlocal problems that feature interactions between points separated by a finite distance. Here, by substructuring it is meant that a…

The marriage of density functional theory (DFT) and deep learning methods has the potential to revolutionize modern computational materials science. Here we develop a deep neural network approach to represent DFT Hamiltonian (DeepH) of…

We develop a new density functional theory (DFT) and formalism for correlated electron systems by taking as reference an interacting electron system that has a ground state wavefunction which obeys exactly the Gutzwiller approximation for…

We present domain decomposition finite element/finite difference method for the solution of hyperbolic equation. The domain decomposition is performed such that finite elements and finite differences are used in different subdomains of the…

Kohn-Sham (KS) density functional theory (DFT) is a very efficient method for calculating various properties of solids as, for instance, the total energy, the electron density, or the electronic band structure. The KS-DFT method leads to…

We introduce the multivariate decomposition finite element method for elliptic PDEs with lognormal diffusion coefficient $a=\exp(Z)$ where $Z$ is a Gaussian random field defined by an infinite series expansion $Z(\boldsymbol{y}) =…

Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations (PDEs). Naturally, reduced-order modeling techniques come at the price of computational accuracy for a decrease in computation…

Density functional theory (DFT) is an incredible success story. The low computational cost, combined with useful (but not yet chemical) accuracy, has made DFT a standard technique in most branches of chemistry and materials science.…

We present in full detail a newly developed formalism enabling density functional perturbation theory (DFPT) calculations from a DFT+$U$ ground state. The implementation includes ultrasoft pseudopotentials and is valid for both insulating…

Dynamic Mode Decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of non-linear systems from experimental datasets. Recently, several attempts have extended DMD to the context of low-rank approximations. This…

We introduce the multivariate decomposition finite element method (MDFEM) for solving elliptic PDEs with uniform random diffusion coefficients. We show that the MDFEM can be used to reduce the computational complexity of estimating the…

Structure factors obtained from diffraction experiments are one of the most important quantities for characterizing the electronic and structural properties of materials. Methods for calculating this quantity from plane-wave density…

Density functional theory (DFT), one of the most widely utilized methods available to computational chemistry, fails to describe systems with statically correlated electrons. To address this shortcoming, in previous work we transformed DFT…

The flat plane condition is the union of two exact constraints in electronic structure theory: i) energetic piecewise linearity with fractional electron removal or addition and ii) invariant energetics with change in electron spin in a half…

The aim of this paper is the derivation of structure preserving schemes for the solution of the EPDiff equation, with particular emphasis on the two dimensional case. We develop three different schemes based on the Discrete Variational…