This book covers finite element methods for several typical eigenvalues that arise from
science and engineering. Both theory and implementation are covered in depth at the …

We present an efficient computational approach to perform real-space electronic structure
calculations using an adaptive higher-order finite-element discretization of Kohn–Sham …

A multigrid method is proposed to solve the eigenvalue problem by the finite element
method based on the combination of the multilevel correction scheme for the eigenvalue …

Density functional theory (DFT) provides the most widely used models for simulating
molecules and materials based on the fundamental laws of quantum mechanics. It earned …

The Kohn--Sham model is a powerful, widely used approach for computation of ground state
electronic energies and densities in chemistry, materials science, biology, and nanoscience …

The density functional theory (DFT) in electronic structure calculations can be formulated as
either a nonlinear eigenvalue or a direct minimization problem. The most widely used …

We introduce a type of full multigrid method for the nonlinear eigenvalue problem. The main
idea is to transform the solution of the nonlinear eigenvalue problem into a series of …

The ground states of Bose–Einstein condensates in a rotating frame can be described as
constrained minimizers of the Gross–Pitaevskii energy functional with an angular …

In this paper, an adaptive finite element method is proposed for solving Kohn–Sham
equation with the multilevel correction technique. In the method, the Kohn–Sham equation is …

In this paper, we study a few theoretical issues in the discretized Kohn--Sham (KS) density
functional theory. The equivalence between either a local or global minimizer of the KS total …