Solvers for $$\mathcal{O} (N)$$ Electronic Structure in the Strong Scaling Limit
Here we present a hybrid OpenMP/Charm\tt++ framework for solving the $$\mathcal{O} (N)$$ selfconsistentfield eigenvalue problem with parallelism in the strong scaling regime, $$P\gg{N}$$, where $P$ is the number of cores, and $N$ is a measure of system size, i.e., the number of matrix rows/columns, basis functions, atoms, molecules, etc. This result is achieved with a nested approach to spectral projection and the sparse approximate matrix multiply [Bock and Challacombe, SIAM J. Sci. Comput., 35 (2013), pp. C72C98], and involves a recursive, taskparallel algorithm, often employed by generalized $N$Body solvers, to occlusion and culling of negligible products in the case of matrices with decay. Lastly, employing classic technologies associated with generalized $N$Body solvers, including overdecomposition, recursive task parallelism, orderings that preserve locality, and persistencebased load balancing, we obtain scaling beyond hundreds of cores per molecule for small water clusters ([H$${}_2$$O]$${}_N$$, $$N \in \{ 30, 90, 150 \}$$, $$P/N \approx \{ 819, 273, 164 \}$$) and find support for an increasingly strong scalability with increasing system size $N$.
 Authors:

^{[1]};
^{[1]};
^{[2]}
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Division
 Univ. of Illinois, UrbanaChampaign, IL (United States). Parallel Programming Lab.
 Publication Date:
 Report Number(s):
 LAUR1422050
Journal ID: ISSN 10648275
 Grant/Contract Number:
 AC5206NA25396; 20110230ER
 Type:
 Accepted Manuscript
 Journal Name:
 SIAM Journal on Scientific Computing
 Additional Journal Information:
 Journal Volume: 38; Journal Issue: 1; Journal ID: ISSN 10648275
 Publisher:
 SIAM
 Research Org:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org:
 USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; sparse approximate matrix multiply; sparse linear algebra; SpAMM; reduced complexity algorithm; linear scaling; quantum chemistry; spectral projection; NBody; Charm++; matrices with decay; parallel irregular; space filling curve; persistence load balancing; overdecomposition
 OSTI Identifier:
 1329852
Bock, Nicolas, Challacombe, William M., and Kale, Laxmikant. Solvers for $\mathcal{O} (N)$ Electronic Structure in the Strong Scaling Limit. United States: N. p.,
Web. doi:10.1137/140974602.
Bock, Nicolas, Challacombe, William M., & Kale, Laxmikant. Solvers for $\mathcal{O} (N)$ Electronic Structure in the Strong Scaling Limit. United States. doi:10.1137/140974602.
Bock, Nicolas, Challacombe, William M., and Kale, Laxmikant. 2016.
"Solvers for $\mathcal{O} (N)$ Electronic Structure in the Strong Scaling Limit". United States.
doi:10.1137/140974602. https://www.osti.gov/servlets/purl/1329852.
@article{osti_1329852,
title = {Solvers for $\mathcal{O} (N)$ Electronic Structure in the Strong Scaling Limit},
author = {Bock, Nicolas and Challacombe, William M. and Kale, Laxmikant},
abstractNote = {Here we present a hybrid OpenMP/Charm\tt++ framework for solving the $\mathcal{O} (N)$ selfconsistentfield eigenvalue problem with parallelism in the strong scaling regime, $P\gg{N}$, where $P$ is the number of cores, and $N$ is a measure of system size, i.e., the number of matrix rows/columns, basis functions, atoms, molecules, etc. This result is achieved with a nested approach to spectral projection and the sparse approximate matrix multiply [Bock and Challacombe, SIAM J. Sci. Comput., 35 (2013), pp. C72C98], and involves a recursive, taskparallel algorithm, often employed by generalized $N$Body solvers, to occlusion and culling of negligible products in the case of matrices with decay. Lastly, employing classic technologies associated with generalized $N$Body solvers, including overdecomposition, recursive task parallelism, orderings that preserve locality, and persistencebased load balancing, we obtain scaling beyond hundreds of cores per molecule for small water clusters ([H${}_2$O]${}_N$, $N \in \{ 30, 90, 150 \}$, $P/N \approx \{ 819, 273, 164 \}$) and find support for an increasingly strong scalability with increasing system size $N$.},
doi = {10.1137/140974602},
journal = {SIAM Journal on Scientific Computing},
number = 1,
volume = 38,
place = {United States},
year = {2016},
month = {1}
}