Isogeometric analysis in electronic structure calculations

@article{Cimrman2016IsogeometricAI,
  title={Isogeometric analysis in electronic structure calculations},
  author={Robert Cimrman and M. G. Novak and Radek Kolman and Miroslav Tuma and Jir{\'i} Vack{\'a}r},
  journal={Math. Comput. Simul.},
  year={2016},
  volume={145},
  pages={125-135}
}
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References

SHOWING 1-10 OF 44 REFERENCES

CORRIGENDUM: Momentum-space formalism for the total energy of solids

A momentum-space formalism for calculating the total energy of solids is derived. This formalism is designed particularly for application with the self-consistent pseudo- potential method. In the…

Studies of Refinement and Continuity in Isogeometric Structural Analysis (Preprint)

Isogeometric analysis of free vibration of simple shaped elastic samples.

The main attention is paid to the comparison of convergence rate, accuracy, and time-consumption of IGA against FEM and also to show a spline order and parameterization effects.

Density functional theory

An overview of the properties that can be calculated with DFT, such as geometries, energies, reaction mechanisms, and spectroscopic properties, is provided.

On the adaptive finite element analysis of the Kohn–Sham equations: methods, algorithms, and implementation

A fully self‐consistent method of solving the quantum many‐body problem within the context of density functional theory using a real‐space method based on finite element discretisation of realspace is considered.

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

B-splines and NURBS based finite element methods for Kohn–Sham equations

Self-Consistent Equations Including Exchange and Correlation Effects

From a theory of Hohenberg and Kohn, approximation methods for treating an inhomogeneous system of interacting electrons are developed. These methods are exact for systems of slowly varying or high…

Complex wavenumber Fourier analysis of the B-spline based finite element method

Electronic Structure: Basic Theory and Practical Methods

Preface Acknowledgements Notation Part I. Overview and Background Topics: 1. Introduction 2. Overview 3. Theoretical background 4. Periodic solids and electron bands 5. Uniform electron gas and…