Efficient isoparametric integration over arbitrary space-filling Voronoi polyhedra for electronic structure calculations

Alam, Aftab; Khan, S. N.; Wilson, Brian G.; Johnson, D. D.

doi:10.1103/PhysRevB.84.045105

Title: Efficient isoparametric integration over arbitrary space-filling Voronoi polyhedra for electronic structure calculations

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Authors:: Alam, Aftab; Khan, S. N.; Wilson, Brian G.; Johnson, D. D.

Publication Date:: Wed Jul 06 00:00:00 EDT 2011

Sponsoring Org.:: USDOE

OSTI Identifier:: 1099721

Resource Type:: Publisher's Accepted Manuscript

Journal Name:: Physical Review B

Additional Journal Information:: Journal Volume: 84; Journal Issue: 4; Journal ID: ISSN 1098-0121

Publisher:: American Physical Society

Country of Publication:: United States

Language:: English

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                    Alam, Aftab, Khan, S. N., Wilson, Brian G., and Johnson, D. D. Efficient isoparametric integration over arbitrary space-filling Voronoi polyhedra for electronic structure calculations.  United States: N. p., 2011. 
Web.  doi:10.1103/PhysRevB.84.045105.

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                    Alam, Aftab, Khan, S. N., Wilson, Brian G., & Johnson, D. D. Efficient isoparametric integration over arbitrary space-filling Voronoi polyhedra for electronic structure calculations.  United States.  https://doi.org/10.1103/PhysRevB.84.045105

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                    Alam, Aftab, Khan, S. N., Wilson, Brian G., and Johnson, D. D. Wed .  
"Efficient isoparametric integration over arbitrary space-filling Voronoi polyhedra for electronic structure calculations".  United States.  https://doi.org/10.1103/PhysRevB.84.045105.

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@article{osti_1099721,

  title        = {Efficient isoparametric integration over arbitrary space-filling Voronoi polyhedra for electronic structure calculations},

  author       = {Alam, Aftab and Khan, S. N. and Wilson, Brian G. and Johnson, D. D.},

  abstractNote = {},

  doi          = {10.1103/PhysRevB.84.045105},

  journal      = {Physical Review B},

  number       = 4,

  volume       = 84,

  place        = {United States},

  year         = {Wed Jul 06 00:00:00 EDT 2011},

  month        = {Wed Jul 06 00:00:00 EDT 2011}

}

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Similar Records in DOE PAGES and OSTI.GOV collections:

Efficient isoparametric integration over arbitrary space-filling Voronoi polyhedra for electronic structure calculations

Journal Article Alam, Aftab ; Khan, S. N. ; Wilson, Brian G. ; ... - Physical Review. B, Condensed Matter and Materials Physics

A numerically efficient, accurate, and easily implemented integration scheme over convex Voronoi polyhedra (VP) is presented for use in ab initio electronic-structure calculations. We combine a weighted Voronoi tessellation with isoparametric integration via Gauss-Legendre quadratures to provide rapidly convergent VP integrals for a variety of integrands, including those with a Coulomb singularity. We showcase the capability of our approach by first applying it to an analytic charge-density model achieving machine-precision accuracy with expected convergence properties in milliseconds. For contrast, we compare our results to those using shape-functions and show our approach is greater than 10⁵ times faster and 10⁷ timesmore »« less
https://doi.org/10.1103/PhysRevB.84.045105
Efficient isoparametric integration over arbitrary space-filling Voronoi polyhedra for electronic structure calculations

Journal Article Alam, Aftab ; Khan, S. N. ; Wilson, Brian G. ; ... - Physical Review. B, Condensed Matter and Materials Physics
https://doi.org/10.1103/PhysRevB.84.045105
Comment on: Accurate and fast numerical solution of Poisson s equation for arbitrary, space-filling Voronoi polyhedra: Near-field corrections revisited

Journal Article Gonis, Antonios ; Zhang, Xiaoguang - Physical Review B

This is a comment on the paper by Aftab Alam, Brian G. Wilson, and D. D. Johnson [1], proposing the solution of the near-field corrections (NFC s) problem for the Poisson equation for extended, e.g., space filling, charge densities. We point out that the problem considered by the authors can be simply avoided by means of performing certain integrals in a particular order, while their method does not address the genuine problem of NFC s that arises when the solution of the Poisson equation is attempted within multiple scattering theory. We also point out a flaw in their line ofmore »« less
https://doi.org/10.1103/PhysRevB.86.127101
Reply to “Comment on ‘Accurate and fast numerical solution of Poisson's equation for arbitrary, space-filling Voronoi polyhedra: Near-field corrections revisited’ ”

Journal Article Alam, Aftab ; Wilson, Brian G. ; Johnson, Duane D. - Physical Review. B, Condensed Matter and Materials Physics

This is a Reply to the Comment by Gonis and Zhang1 on our recent paper.2 They discuss supposed issues with our “accurate and fast numerical solution of Poisson’s equation for arbitrary Voronoi polyhedra” (VP). The method of Gonis et al.3 and Vitos and Koll´ar4 correctly addresses the mathematical issues related to the solution of Poisson’s equation [and near-field corrections (NFCs)] using a spherical harmonic basis (L’s). However, as discussed in Ref. 2, their method is not numerically efficient and suffers from severe convergence issues from the multiply nested (conditionally convergent) multipole expansions to address r</r> problems. Hence, the abstract inmore »« less
https://doi.org/10.1103/PhysRevB.86.127102
Accurate and fast numerical solution of Poisson s equation for arbitrary, space-filling Voronoi polyhedra: Near-field corrections revisited

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We present an accurate and rapid solution of Poisson s equation for space-filling, arbitrarily shaped, convex Voronoi polyhedra (VP); the method is O(NVP), where NVP is the number of distinct VP representing the system. In effect, we resolve the long-standing problem of fast but accurate numerical solution of the near-field corrections, contributions to the potential due to near VP typically those involving multipole-type conditionally convergent sums, or use of fast Fourier transforms. Our method avoids all ill-convergent sums, is simple, accurate, efficient, and works generally, i.e., for periodic solids, molecules, or systems with disorder or imperfections. We demonstrate the practicalitymore »« less
https://doi.org/10.1103/PhysRevB.84.205106

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