1996/06/21 by E. L. Briggs, Briggs, E. L., D. J. Sullivan +3
Earth and Planetary Sciences · Materials Science · Physics and Astronomy · #Advanced Chemical Physics Studies #Electron and X-Ray Spectroscopy Techniques #FOS: Physical sciences #High-pressure geophysics and materials #Materials Science (cond-mat.mtrl-sci) #cond-mat.mtrl-sci #mtrl-th
paper · pdf · doi:10.48550/arxiv.mtrl-th/9606002
RevTeX preprint format, 41 pages, 4 postscript figures
arxiv created 1996/06/21 · openalex publication_date 1996/06/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We describe a set of techniques for performing large scale ab initio calculations using multigrid accelerations and a real-space grid as a basis. The multigrid methods provide effective convergence acceleration and preconditioning on all length scales, thereby permitting efficient calculations for ill-conditioned systems with long length scales or high energy cut-offs. We discuss specific implementations of multigrid and real-space algorithms for electronic structure calculations, including an efficient multigrid-accelerated solver for Kohn-Sham equations, compact yet accurate discretization schemes for the Kohn-Sham and Poisson equations, optimized pseudo\-potentials for real-space calculations, efficacious computation of ionic forces, and a complex-wavefunction implementation for arbitrary sampling of the Brillioun zone. A particular strength of a real-space multigrid approach is its ready adaptability to massively parallel computer architectures, and we present an implementation for the Cray-T3D with essentially linear scaling of the execution time with the number of processors. The method has been applied to a variety of periodic and non-periodic systems, including disordered Si, a N impurity in diamond, AlN in the wurtzite structure, and bulk Al. The high accuracy of the atomic forces allows for large step molecular dynamics; e.g., in a 1 ps simulation of Si at 1100 K with an ionic step of 80 a.u., the total energy was conserved within 27 microeV per atom.