- https://www.mdpi.com/1999-4893/12/9/187
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Research output: Contribution to journal › Journal article

Published

**Using graph partitioning for scalable distributed quantum molecular dynamics.** / Djidjev, H.N.; Hahn, G.; Mniszewski, S.M.; Negre, C.F.A.; Niklasson, A.M.N.

Research output: Contribution to journal › Journal article

Djidjev, HN, Hahn, G, Mniszewski, SM, Negre, CFA & Niklasson, AMN 2019, 'Using graph partitioning for scalable distributed quantum molecular dynamics', *Numerical Algorithms*, vol. 12, no. 9, 187. https://doi.org/10.3390/a12090187

Djidjev, H. N., Hahn, G., Mniszewski, S. M., Negre, C. F. A., & Niklasson, A. M. N. (2019). Using graph partitioning for scalable distributed quantum molecular dynamics. *Numerical Algorithms*, *12*(9), [187]. https://doi.org/10.3390/a12090187

Djidjev HN, Hahn G, Mniszewski SM, Negre CFA, Niklasson AMN. Using graph partitioning for scalable distributed quantum molecular dynamics. Numerical Algorithms. 2019 Sep 7;12(9). 187. https://doi.org/10.3390/a12090187

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title = "Using graph partitioning for scalable distributed quantum molecular dynamics",

abstract = "The simulation of the physical movement of multi-body systems at an atomistic level, with forces calculated from a quantum mechanical description of the electrons, motivates a graph partitioning problem studied in this article. Several advanced algorithms relying on evaluations of matrix polynomials have been published in the literature for such simulations. We aim to use a special type of graph partitioning to efficiently parallelize these computations. For this, we create a graph representing the zero–nonzero structure of a thresholded density matrix, and partition that graph into several components. Each separate submatrix (corresponding to each subgraph) is then substituted into the matrix polynomial, and the result for the full matrix polynomial is reassembled at the end from the individual polynomials. This paper starts by introducing a rigorous definition as well as a mathematical justification of this partitioning problem. We assess the performance of several methods to compute graph partitions with respect to both the quality of the partitioning and their runtime.",

keywords = "density matrix, G-SP2, graph partitioning, molecular dynamics, QMD, SP2 algorithm",

author = "H.N. Djidjev and G. Hahn and S.M. Mniszewski and C.F.A. Negre and A.M.N. Niklasson",

year = "2019",

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AU - Djidjev, H.N.

AU - Hahn, G.

AU - Mniszewski, S.M.

AU - Negre, C.F.A.

AU - Niklasson, A.M.N.

PY - 2019/9/7

Y1 - 2019/9/7

N2 - The simulation of the physical movement of multi-body systems at an atomistic level, with forces calculated from a quantum mechanical description of the electrons, motivates a graph partitioning problem studied in this article. Several advanced algorithms relying on evaluations of matrix polynomials have been published in the literature for such simulations. We aim to use a special type of graph partitioning to efficiently parallelize these computations. For this, we create a graph representing the zero–nonzero structure of a thresholded density matrix, and partition that graph into several components. Each separate submatrix (corresponding to each subgraph) is then substituted into the matrix polynomial, and the result for the full matrix polynomial is reassembled at the end from the individual polynomials. This paper starts by introducing a rigorous definition as well as a mathematical justification of this partitioning problem. We assess the performance of several methods to compute graph partitions with respect to both the quality of the partitioning and their runtime.

AB - The simulation of the physical movement of multi-body systems at an atomistic level, with forces calculated from a quantum mechanical description of the electrons, motivates a graph partitioning problem studied in this article. Several advanced algorithms relying on evaluations of matrix polynomials have been published in the literature for such simulations. We aim to use a special type of graph partitioning to efficiently parallelize these computations. For this, we create a graph representing the zero–nonzero structure of a thresholded density matrix, and partition that graph into several components. Each separate submatrix (corresponding to each subgraph) is then substituted into the matrix polynomial, and the result for the full matrix polynomial is reassembled at the end from the individual polynomials. This paper starts by introducing a rigorous definition as well as a mathematical justification of this partitioning problem. We assess the performance of several methods to compute graph partitions with respect to both the quality of the partitioning and their runtime.

KW - density matrix

KW - G-SP2

KW - graph partitioning

KW - molecular dynamics

KW - QMD

KW - SP2 algorithm

U2 - 10.3390/a12090187

DO - 10.3390/a12090187

M3 - Journal article

VL - 12

JO - Numerical Algorithms

JF - Numerical Algorithms

SN - 1017-1398

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ER -