Real-space multigrid methods for large-scale electronic structure problems

✍ Scribed by J. Bernholc; E. L. Briggs; D. J. Sullivan; C. J. Brabec; M. Buongiorno Nardelli; K. Rapcewicz; C. Roland; M. Wensell

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 314 KB
• Volume: 65
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/(sici)1097-461x(1997)65:5<531::aid-qua18>3.0.co;2-5

✦ Synopsis

We describe the development and applications of a new electronic structure method that uses a real-space grid as a basis. Multigrid techniques provide preconditioning and convergence acceleration at all length scales and therefore lead to Ž . particularly efficient algorithms. The salient points of our implementation include: i new compact discretization schemes in real space for systems with cubic, orthorhombic, Ž . and hexagonal symmetry and ii new multilevel algorithms for the iterative solution of Kohn᎐Sham and Poisson equations. The accuracy of the discretizations was tested by direct comparison with plane-wave calculations, when possible, and the results were in excellent agreement in all cases. These techniques are very suitable for use on massively Ž . parallel computers and in O N methods. Tests on the Cray-T3D have shown nearly Ž . linear scaling of the execution time up to the maximum number of processors 512 . The above methodology was tested on a large number of systems, such as the C molecule, 60 diamond, Si and GaN supercells, and quantum molecular dynamics simulations for Si. Large-scale applications include a simulation of surface melting of Si and investigations of electronic and structural properties of surfaces, interfaces, and biomolecules.