Efficient O ( N ) integration for all-electron electronic structure calculation using numeric basis functions

• Published in: Journal of computational physics Vol. 228; no. 22; pp. 8367 - 8379
• Main Authors: Havu, V., Blum, V., Havu, P., Scheffler, M.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Inc 01.12.2009; Elsevier
• Subjects: ALGORITHMS; Atom-centered basis functions; Computational techniques; DENSITY FUNCTIONAL METHOD; Density functional theory; ELECTRONIC STRUCTURE; Electronic structure theory; ELECTRONS; Exact sciences and technology; FUNCTIONS; MATHEMATICAL METHODS AND COMPUTING; Mathematical methods in physics; Numerical integration grid; Physics; Spatial partitioning; 71.15.Dx; 02.60.Jh; 71.15.Ap; Density functional theory; Spatial partitioning; Electronic structure theory; Atom-centered basis functions; Numerical integration grid; Numerical integration; Calculation methods; Algorithms; Density functional method; Calculation; Performance
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2009.08.008

We consider the problem of developing O ( N ) scaling grid-based operations needed in many central operations when performing electronic structure calculations with numeric atom-centered orbitals as basis functions. We outline the overall formulation of localized algorithms, and specifically the creation of localized grid batches. The choice of the grid partitioning scheme plays an important role in the performance and memory consumption of the grid-based operations. Three different top-down partitioning methods are investigated, and compared with formally more rigorous yet much more expensive bottom-up algorithms. We show that a conceptually simple top-down grid partitioning scheme achieves essentially the same efficiency as the more rigorous bottom-up approaches.