%0 Journal Article
%J Physical Review B
%D 2011
%T Efficient isoparametric integration over arbitrary space-filling Voronoi polyhedra for electronic structure calculations
%A Alam, A.
%A Khan, S. N.
%A Wilson, B. G.
%A Johnson, D. D.
%M WOS:000292512500002
%P 045105
%R 10.1103/PhysRevB.84.045105
%V 84
%X 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 10(5) times faster and 10(7) times more accurate. A weighted Voronoi tessellation also allows for a physics-based partitioning of space that guarantees convex, space-filling VP while reflecting accurate atomic size and site charges, as we show within KKR methods applied to Fe-Pd alloys.
%Z Alam, Aftab Khan, S. N. Wilson, Brian G. Johnson, D. D.
%8 07
%@ 1098-0121