Real-space multigrid solution of electrostatics problems and the Kohn–Sham equations

✍ Scribed by Thomas L. Beck

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 195 KB
• Volume: 65
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/(sici)1097-461x(1997)65:5<477::aid-qua12>3.0.co;2-0

✦ Synopsis

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 Ž . 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.