Higher-order adaptive finite-element methods for Kohn-Sham density functional theory

  title={Higher-order adaptive finite-element methods for Kohn-Sham density functional theory},
  author={Phani Motamarri and Michael R. Nowak and Kenneth W. Leiter and Jaroslaw Knap and Vikram Gavini},
  journal={J. Comput. Phys.},

Real time time-dependent density functional theory using higher order finite-element methods

This work develops an a priori mesh adaption technique, based on the semi-discrete error estimate on the time-dependent Kohn-Sham orbitals, to construct a close to optimal finite-element discretization, and demonstrates a staggering 100-fold reduction in the computational time afforded by higher-order finite-elements over linear finite-Elements.

Large-scale Real-space Kohn-Sham Density Functional Theory Calculations Using Adaptive Finite-element Discretization.

This thesis tries to address the inherent shortcomings of finite-element discretization for DFT and presents the development of new computationally efficient and robust parallel algorithms to enable large-scale DFT calculations.

Adaptive Finite Element Approximations for Kohn-Sham Models

An adaptive finite element algorithm with a quite general marking strategy is introduced and the convergence rate and quasi-optimal complexity of the Kohn-Sham model approximations are proved.

Real-time adaptive finite element solution of time-dependent Kohn-Sham equation

A spectral scheme for Kohn-Sham density functional theory of clusters

Large-scale all-electron density functional theory calculations using an enriched finite-element basis

The accuracy, efficiency and parallel scalability of the proposed method on semiconducting and heavy-metallic systems of various sizes, with the largest system containing 8694 electrons, are demonstrated.

An Asymptotics-Based Adaptive Finite Element Method for Kohn–Sham Equation

An a posteriori error estimation for Kohn–Sham equation by coarsening mesh is proposed and an upper bound for the difference of the total energies on two successively refined meshes is derived by the numerical solutions on two meshes through an asymptotic analysis.



Higher-order adaptive finite-element methods for orbital-free density functional theory

Adaptive Finite Element Method for Solving the Exact Kohn-Sham Equation of Density Functional Theory.

Results of the application of an adaptive finite element (FE) based solution using the FETK library of M. Holst to Density Functional Theory (DFT) approximation to the electronic structure of atoms

Real-space mesh techniques in density-functional theory

Real-space methods for solving self-consistent eigenvalue problems in real space have found recent application in computations of optical response and excited states in time-dependent density-functional theory, and these computational developments are summarized.

Finite-element methods in electronic-structure theory

Parallel self-consistent-field calculations via Chebyshev-filtered subspace acceleration.

An approach for implementing a nonlinear Chebyshev-filtered subspace iteration method, which avoids computing explicit eigenvectors except at the first self-consistent-field (SCF) iteration, and results in a significant speedup over methods based on standard diagonalization.

A Kohn-Sham equation solver based on hexahedral finite elements

An h-adaptive finite element solver for the calculations of the electronic structures