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

TitleEfficient isoparametric integration over arbitrary space-filling Voronoi polyhedra for electronic structure calculations
Publication TypeJournal Article
Year of Publication2011
AuthorsAlam A, Khan SN, Wilson BG, Johnson DD
Journal TitlePhysical Review B
Volume84
Pages045105
Date Published07
ISBN Number1098-0121
Accession NumberWOS:000292512500002
Abstract

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.

DOI10.1103/PhysRevB.84.045105