Domain Decomposition and Electronic Structure Computations: A Promising Approach

Numerical methods for Kohn–Sham density functional theory

“…Chen and Lu (2016) for a mathematical analysis of the divide-and-conquer method, based on the analysis tools developed in . Further developments of the divide-and-conquer method and related domain decomposition type method can be found in Yang and Lee (1995), , , Barrault, Cancès, Hager and Le Bris (2007) and Bencteux et al (2008). A great advantage of the method lies in the intrinsic parallelism of the computation for each subsystem, which has been utilized for large-scale calculations with more than 10 6 atoms and 10 12 electronic degrees of freedom (Kobayashi and Nakai 2009, Ohba et al 2012, Shimojo, Kalia, Nakano and Vashishta 2008, Shimojo et al 2011.…”

“…Further developments of the divide-and-conquer method and related domain decomposition type method can be found in Yang and Lee (1995), Wang, Zhao and Meza (2008), Zhao, Meza and Wang (2008), Barrault, Cancès, Hager and Le Bris (2007) and Bencteux et al. (2008). A great advantage of the method lies in the intrinsic parallelism of the computation for each subsystem, which has been utilized for large-scale calculations with more than atoms and electronic degrees of freedom (Kobayashi and Nakai 2009, Ohba et al.…”