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

@article{Motamarri2012HigherorderAF, title={Higher-order adaptive finite-element methods for orbital-free density functional theory}, author={Phani Motamarri and Mrinal Iyer and Jaroslaw Knap and Vikram Gavini}, journal={J. Comput. Phys.}, year={2012}, volume={231}, pages={6596-6621} }

## 32 Citations

### Higher-order finite-difference formulation of periodic Orbital-free Density Functional Theory

- Computer ScienceJ. Comput. Phys.
- 2016

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

- Computer ScienceJ. Comput. Phys.
- 2013

### NURBS-based non-periodic finite element framework for Kohn-Sham density functional theory calculations

- PhysicsJ. Comput. Phys.
- 2020

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

- Computer SciencePhysical Review B
- 2019

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.

- Computer Science
- 2014

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.

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

- Computer Science
- 2017

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.

### SPARC: Accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory: Isolated clusters

- Computer ScienceComput. Phys. Commun.
- 2017

### Atom-partitioned multipole expansions for electrostatic potential boundary conditions

- Computer ScienceJ. Comput. Phys.
- 2017

### Configurational forces in electronic structure calculations using Kohn-Sham density functional theory

- Physics
- 2017

We derive the expressions for configurational forces in Kohn-Sham density functional theory, which correspond to the generalized variational force computed as the derivative of the Kohn-Sham energyâ€¦

### Convergence of a Strang splitting finite element discretization for the Schr\"odinger-Poisson equation

- Mathematics
- 2016

Operator splitting methods combined with finite element spatial discretizations are studied for time-dependent nonlinear Schr\"odinger equations. In particular, the Schr\"odinger-Poisson equationâ€¦

## References

SHOWING 1-10 OF 55 REFERENCES

### Non-periodic finite-element formulation of Kohnâ€“Sham density functional theory

- Computer Science
- 2010

### Non-periodic finite-element formulation of orbital-free density functional theory

- Computer Science
- 2006

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

- Computer ScienceJournal of chemical theory and computation
- 2009

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 atomsâ€¦

### Real-space mesh techniques in density-functional theory

- Computer Science
- 2000

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 method for electronic structure.

- Computer SciencePhysical review. B, Condensed matter
- 1989

Algorithms, including the highly efficient multigrid method, for solving the Poisson equation and for the ground state of the single-particle Schroedinger equation in O(N) time are discussed.

### An Efficient Real Space Method for Orbital-Free Density-Functional Theory

- Computer Science
- 2006

It is proved that the energy minimizer satisfies a second order quasilinear elliptic equation, even at the points where the electron density vanishes, and an efficient real space method is presented for Orbital-Free Density Functional Theory.

### All-electron density functional theory and time-dependent density functional theory with high-order finite elements.

- Physics, Computer ScienceThe Journal of chemical physics
- 2009

This work presents an all-electron method which employs high-order hierarchical finite-element bases, in which structured atomic meshes are merged to an unstructured molecular mesh, and allows a highly nonuniform discretization of the space.

### Computational method for general multicenter electronic structure calculations.

- ChemistryPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 2000

Here a three-dimensional fully numerical method is formulated and applied to the calculation of the electronic structure of general multicenter Hamiltonian systems, and local density approximations are presented for selected subsets of atomic and diatomic molecules as well as the ozone molecule.