Taskbased Parallel Computation of the Density Matrix in Quantumbased Molecular Dynamics using Graph Partitioning
Abstract
Quantumbased molecular dynamics (QMD) is a highly accurate and transferable method for material science simulations. However, the time scales and system sizes accessible to QMD are typically limited to picoseconds and a few hundred atoms. These constraints arise due to expensive selfconsistent groundstate electronic structure calculations that can often scale cubically with the number of atoms. Linearly scaling methods depend on computing the density matrix P from the Hamiltonian matrix H by exploiting the sparsity in both matrices. The secondorder spectral projection (SP2) algorithm is an O(N) algorithm that computes P with a sequence of 40  50 matrixmatrix multiplications. In this paper, we present taskbased implementations of a recently developed dataparallel graphbased approach to the SP2 algorithm, GSP2. We represent the density matrix P as an undirected graph and use graph partitioning techniques to divide the computation into smaller independent tasks. The partitions thus obtained are generally not of equal size and give rise to undesirable load imbalances in standard MPIbased implementations. This loadbalancing challenge can be mitigated by dynamically scheduling parallel computations at runtime using taskbased programming models. We develop taskbased implementations of the dataparallel GSP2 algorithm using both Intel's Concurrent Collections (CnC) as well as the Charm++more »
 Authors:

 Univ. of Illinois, UrbanaChampaign, IL (United States)
 Univ. of Missouri, Columbia, MO (United States)
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Univ. of Delaware, Newark, DE (United States)
 Univ. of Iowa, Iowa City, IA (United States)
 Univ. of Georgia, Athens, GA (United States)
 Columbia Univ., New York, NY (United States)
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC). Advanced Scientific Computing Research (ASCR) (SC21)
 OSTI Identifier:
 1501801
 Report Number(s):
 LAUR1624908
Journal ID: ISSN 10648275
 Grant/Contract Number:
 89233218CNA000001
 Resource Type:
 Accepted Manuscript
 Journal Name:
 SIAM Journal on Scientific Computing
 Additional Journal Information:
 Journal Volume: 39; Journal Issue: 6; Journal ID: ISSN 10648275
 Publisher:
 SIAM
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Computer Science; Mathematics
Citation Formats
Ghale, Purnima, Kroonblawd, Matthew P., Mniszewski, Sue, Negre, Christian F. A., Pavel, Robert, Pino, Sergio, Sardeshmukh, Vivek, Shi, Guangjie, and Hahn, Georg. Taskbased Parallel Computation of the Density Matrix in Quantumbased Molecular Dynamics using Graph Partitioning. United States: N. p., 2017.
Web. doi:10.1137/16M109404X.
Ghale, Purnima, Kroonblawd, Matthew P., Mniszewski, Sue, Negre, Christian F. A., Pavel, Robert, Pino, Sergio, Sardeshmukh, Vivek, Shi, Guangjie, & Hahn, Georg. Taskbased Parallel Computation of the Density Matrix in Quantumbased Molecular Dynamics using Graph Partitioning. United States. doi:10.1137/16M109404X.
Ghale, Purnima, Kroonblawd, Matthew P., Mniszewski, Sue, Negre, Christian F. A., Pavel, Robert, Pino, Sergio, Sardeshmukh, Vivek, Shi, Guangjie, and Hahn, Georg. Thu .
"Taskbased Parallel Computation of the Density Matrix in Quantumbased Molecular Dynamics using Graph Partitioning". United States. doi:10.1137/16M109404X. https://www.osti.gov/servlets/purl/1501801.
@article{osti_1501801,
title = {Taskbased Parallel Computation of the Density Matrix in Quantumbased Molecular Dynamics using Graph Partitioning},
author = {Ghale, Purnima and Kroonblawd, Matthew P. and Mniszewski, Sue and Negre, Christian F. A. and Pavel, Robert and Pino, Sergio and Sardeshmukh, Vivek and Shi, Guangjie and Hahn, Georg},
abstractNote = {Quantumbased molecular dynamics (QMD) is a highly accurate and transferable method for material science simulations. However, the time scales and system sizes accessible to QMD are typically limited to picoseconds and a few hundred atoms. These constraints arise due to expensive selfconsistent groundstate electronic structure calculations that can often scale cubically with the number of atoms. Linearly scaling methods depend on computing the density matrix P from the Hamiltonian matrix H by exploiting the sparsity in both matrices. The secondorder spectral projection (SP2) algorithm is an O(N) algorithm that computes P with a sequence of 40  50 matrixmatrix multiplications. In this paper, we present taskbased implementations of a recently developed dataparallel graphbased approach to the SP2 algorithm, GSP2. We represent the density matrix P as an undirected graph and use graph partitioning techniques to divide the computation into smaller independent tasks. The partitions thus obtained are generally not of equal size and give rise to undesirable load imbalances in standard MPIbased implementations. This loadbalancing challenge can be mitigated by dynamically scheduling parallel computations at runtime using taskbased programming models. We develop taskbased implementations of the dataparallel GSP2 algorithm using both Intel's Concurrent Collections (CnC) as well as the Charm++ programming model and evaluate these implementations for future use. Scaling and performance results of our implementations are investigated for representative segments of QMD simulations for solvated protein systems containing more than 10,000 atoms.},
doi = {10.1137/16M109404X},
journal = {SIAM Journal on Scientific Computing},
number = 6,
volume = 39,
place = {United States},
year = {2017},
month = {12}
}