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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.554 SNIP: 0.82 CiteScore™: 2

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2011002201
pages 83-99


J. E. Pask
Condensed Matter and Materials Division, Lawrence Livermore National Laboratory, Livermore,CA 94550
N. Sukumar
University of California Davis
S. E. Mousavi
Department of Civil and Environmental Engineering, University of California, Davis, CA 95616


We present a linear scaling formulation for the solution of the all-electron Coulomb problem in crystalline solids. The resulting method is systematically improvable and well suited to large-scale quantum mechanical calculations in which the Coulomb potential and energy of a continuous electronic density and singular nuclear density are required. Linear scaling is achieved by introducing smooth, strictly local neutralizing densities to render nuclear interactions strictly local, and solving the remaining neutral Poisson problem for the electrons in real space. Although the formulation includes singular nuclear potentials without smearing approximations, the required Poisson solution is in Sobolev space H1, as required for convergence in the energy norm. We employ enriched finite elements, with enrichments from isolated atom solutions, for an efficient solution of the resulting Poisson problem in the interacting solid. We demonstrate the accuracy and convergence of the approach by direct comparison to standard Ewald sums for a lattice of point charges and demonstrate the accuracy in all-electron quantum mechanical calculations with an application to crystalline diamond.


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