Accurate and fast numerical solution of Poisson's equation for arbitrary, space-filling Voronoi polyhedra: Near-field corrections revisited

TitleAccurate and fast numerical solution of Poisson's equation for arbitrary, space-filling Voronoi polyhedra: Near-field corrections revisited
Publication TypeJournal Article
Year of Publication2011
AuthorsAlam A, Wilson BG, Johnson DD
Journal TitlePhysical Review B
Volume84
Pages205106
Date Published11
Type of ArticleArticle
ISBN Number1098-0121
Accession NumberWOS:000296879100002
Keywordscells, charge-densities, expansion, shape truncation functions, solids, spherical harmonics, systems
Abstract

We present an accurate and rapid solution of Poisson's equation for space-filling, arbitrarily shaped, convex Voronoi polyhedra (VP); the method is O(N(VP)), where N(VP) 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 practicality of the method by numerical calculations compared to exactly solvable models.

DOI10.1103/PhysRevB.84.205106
Alternate JournalPhys. Rev. B