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Real‐space multigrid solution of electrostatics problems and the Kohn–Sham equations
Author(s) -
Beck Thomas L.
Publication year - 1997
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/(sici)1097-461x(1997)65:5<477::aid-qua12>3.0.co;2-0
Subject(s) - kohn–sham equations , multigrid method , poisson–boltzmann equation , poisson's equation , electrostatics , nonlinear system , laplace operator , cartesian coordinate system , space (punctuation) , grid , physics , mathematics , statistical physics , quantum mechanics , density functional theory , computer science , geometry , ion , operating system
A multigrid method for numerically solving electrostatics and quantum chemical problems in real space is discussed. Multigrid techniques are used to solve both the linear Poisson equation and the nonlinear Kohn–Sham and Poisson–Boltzmann equations. The electrostatic potential, Laplacian, charge densities (electrons and nuclei), Kohn–Sham DFT orbitals, and the self‐consistent field potential are all represented discretely on the Cartesian grid. High‐order finite differences are utilized to obtain physically reasonable results on modestly sized grids. The method is summarized and numerical results for all‐electron atomic and molecular structure are presented. The strengths and weaknesses of the method are discussed with suggested directions for future developments, including a new high‐order conservative differencing scheme for accurate composite grid computations which preserves the linear scaling property of the multigrid method. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65 : 477–486, 1997