# Partition of unity finite element method for quantum mechanical materials calculations

@article{Pask2016PartitionOU, title={Partition of unity finite element method for quantum mechanical materials calculations}, author={John E. Pask and N. Sukumar}, journal={Extreme Mechanics Letters}, year={2016}, volume={11}, pages={8-17} }

## 19 Citations

### Fast and robust all-electron density functional theory calculations in solids using orthogonalized enriched finite elements

- Computer SciencePhysical Review B
- 2021

It is demonstrated that the orthogonalized enriched FE basis outperforms the LAPW+lo basis in terms of computational efficiency for and beyond modest sized systems.

### 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.

### Radial and three-dimensional nonlocal pseudopotential calculations in gradient-corrected Kohn–Sham density functional theory based on higher-order finite element methods

- Computer Science
- 2021

### 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.

### Algorithms and Data Structures for Matrix-Free Finite Element Operators with MPI-Parallel Sparse Multi-Vectors

- Computer ScienceACM Trans. Parallel Comput.
- 2020

This work proposes a numerically efficient implementation of sparse parallel vectors within the open-source finite element library deal with the main algorithmic ingredient the matrix-free evaluation of the Hamiltonian operator by cell-wise quadrature.

### Ionic forces and stress tensor in all-electron density functional theory calculations using an enriched finite-element basis

- PhysicsPhysical Review B
- 2022

The enriched ﬁnite element basis—wherein the ﬁnite element basis is enriched with atom-centered numerical functions—has recently been shown to be a computationally eﬃcient basis for systemati-cally…

### Accurate approximations of density functional theory for large systems with applications to defects in crystalline solids

- Materials Science
- 2021

This chapter presents controlled approximations of Kohn-Sham density functional theory (DFT) that enable very large scale simulations. The work is motivated by the study of defects in crystalline…

### Matrix‐Free Locally Adaptive Finite Element Solution of Density‐Functional Theory With Nonorthogonal Orbitals and Multigrid Preconditioning

- Computer Sciencephysica status solidi (b)
- 2018

The proposed method provides a solid framework toward O(N) complexity for the locally adaptive real‐space solution of density functional theory with infinite elements with finite elements with matrix‐free operator evaluation.

### Convergence study of isogeometric analysis based on Bézier extraction in electronic structure calculations

- Computer ScienceAppl. Math. Comput.
- 2018

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