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Title: Solvers for $$\mathcal{O} (N)$$ Electronic Structure in the Strong Scaling Limit

Here we present a hybrid OpenMP/Charm\tt++ framework for solving the $$\mathcal{O} (N)$$ self-consistent-field 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. C72--C98], and involves a recursive, task-parallel 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 persistence-based 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]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Division
  2. Univ. of Illinois, Urbana-Champaign, IL (United States). Parallel Programming Lab.
Publication Date:
Report Number(s):
LA-UR-14-22050
Journal ID: ISSN 1064-8275
Grant/Contract Number:
AC52-06NA25396; 20110230ER
Type:
Accepted Manuscript
Journal Name:
SIAM Journal on Scientific Computing
Additional Journal Information:
Journal Volume: 38; Journal Issue: 1; Journal ID: ISSN 1064-8275
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; N-Body; 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 $\mathcal{O} (N)$ self-consistent-field 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. C72--C98], and involves a recursive, task-parallel 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 persistence-based 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}
}