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Efficient \(O(N)\) integration for all-electron electronic structure calculation using numeric basis functions. (English) Zbl 1180.82004
Summary: 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.

MSC:
82-08 Computational methods (statistical mechanics) (MSC2010)
82B80 Numerical methods in equilibrium statistical mechanics (MSC2010)
81V45 Atomic physics
Software:
QMG; SIESTA; ONETEP; Qhull; METIS
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References:
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