Efficient solution of Poisson's equation with free boundary conditions.

@article{Genovese2006EfficientSO,
  title={Efficient solution of Poisson's equation with free boundary conditions.},
  author={Luigi Genovese and Thierry Deutsch and Alexey I. Neelov and Stefan Goedecker and Gregory Beylkin},
  journal={The Journal of chemical physics},
  year={2006},
  volume={125 7},
  pages={
          074105
        }
}
Interpolating scaling functions give a faithful representation of a localized charge distribution by its values on a grid. For such charge distributions, using a fast Fourier method, we obtain highly accurate electrostatic potentials for free boundary conditions at the cost of O(N log N) operations, where N is the number of grid points. Thus, with our approach, free boundary conditions are treated as efficiently as the periodic conditions via plane wave methods. 

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References

SHOWING 1-10 OF 42 REFERENCES
Linear scaling solution of the coulomb problem using wavelets
Multiresolution quantum chemistry: basic theory and initial applications.
TLDR
A multiresolution solver for the all-electron local density approximation Kohn-Sham equations for general polyatomic molecules to a user-specified precision and the computational cost of applying all operators scales linearly with the number of parameters.
Algorithms for Numerical Analysis in High Dimensions
TLDR
This paper further develops the separated representation by discussing the variety of mechanisms that allow it to be surprisingly efficient; addressing the issue of conditioning; and presenting algorithms for solving linear systems within this framework.
A fast algorithm for particle simulations
Fast evaluation of the Coulomb energy for electron densities
The evaluation of the Coulomb interaction of the electron density with itself dominates the cost of a density-functional theory calculation, due to its quadratic scaling with the size of the system.
Real-space local polynomial basis for solid-state electronic-structure calculations: A finite-element approach
TLDR
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.
A reciprocal space based method for treating long range interactions in ab initio and force-field-based calculations in clusters
A new reciprocal space based formalism for treating long range forces in clusters is presented. It will be shown how the new formalism can be incorporated into plane-wave based density function
A dual length scale method for plane-wave-based, simulation studies of chemical systems modeled using mixed ab initio/empirical force field descriptions
Mixed ab initio/empirical force-field simulation studies, calculations in which one part of the system is treated using a fully ab initio description and another part is treated using an empirical
Accurate molecular integrals and energies using combined plane wave and Gaussian basis sets in molecular electronic structure theory
This paper introduces two developments for the application of plane wave basis sets for accurate molecular calculations. (1) An analytical formula is introduced for the momentum space representation
...
...