@article {5785,
title = {Accurate and fast numerical solution of Poisson{\textquoteright}s equation for arbitrary, space-filling Voronoi polyhedra: Near-field corrections revisited},
journal = {Physical Review B},
volume = {84},
number = {20},
year = {2011},
note = {Alam, Aftab Wilson, Brian G. Johnson, D. D.US Department of Energy, Office of Basic Energy Science, Division of Materials Science and Engineering Division[DEFG02-03ER46026, DE-AC02-07CH11358]; Center for Defect Physics, an Energy Frontier Research Center; US DOE by Lawrence Livermore National Laboratory[DE-AC52-07NA27344]Research sponsored by the US Department of Energy, Office of Basic Energy Science, Division of Materials Science and Engineering Division, from contracts DEFG02-03ER46026, DE-AC02-07CH11358 with Ames Laboratory, which is operated for DOE by Iowa State University under; and the Center for Defect Physics, an Energy Frontier Research Center. Work performed by B. G. W. was under the auspices of the US DOE by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344. We also benefited from discussion with W. A. Shelton in our DOE/BES Computational Materials and Chemical Sciences Network, and from D. M. C. Nicholson in the EFRC, in reproducing their method and results in Ref. 8.29Amer physical socCollege pk846ed},
month = {11},
pages = {205106},
type = {Article},
abstract = {We present an accurate and rapid solution of Poisson{\textquoteright}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.},
keywords = {cells, charge-densities, expansion, shape truncation functions, solids, spherical harmonics, systems},
isbn = {1098-0121},
doi = {10.1103/PhysRevB.84.205106},
author = {Alam, A. and Wilson, B. G. and Johnson, D. D.}
}