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}
}

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References

SHOWING 1-10 OF 77 REFERENCES

Partition-of-unity finite-element method for large scale quantum molecular dynamics on massively parallel computational platforms

Over the course of the past two decades, quantum mechanical calculations have emerged as a key component of modern materials research. However, the solution of the required quantum mechanical

Real-space local polynomial basis for solid-state electronic-structure calculations: A finite-element approach

An approach to solid-state electronic-structure calculations based on the finite-element method that combines the significant advantages of both real-space-grid and basis-oriented approaches and so promises to be particularly well suited for large, accurate calculations.

Gaussian finite-element mixed-basis method for electronic structure calculations

As a fully flexible basis function, the finite element (FE) function was introduced for the representation of the wave function in the molecular electronic state calculation within the density

Finite element methods in ab initio electronic structure calculations

The construction and properties of the required FE bases and their use in the self-consistent solution of the Kohn–Sham equations of density functional theory are reviewed.

Finite-element method for electronic structure.

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.

Real-space pseudopotential method for computing the electronic properties of periodic systems

We present a real-space method for electronic-structure calculations of periodic systems. Our method is based on the self-consistent solution of the Kohn-Sham equations on a uniform three-dimensional

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
...