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Using Graph Partitioning for Scalable Distributed Quantum Molecular Dynamics

Los Alamos National Laboratory, Los Alamos, NM 87544, USA
Department of Mathematics and Statistics, Lancaster University, Bailrigg, Lancaster LA1 4YW, UK
Author to whom correspondence should be addressed.
Part of the work was done when the author was visiting Los Alamos National Laboratory.
Algorithms 2019, 12(9), 187;
Received: 26 June 2019 / Revised: 5 September 2019 / Accepted: 5 September 2019 / Published: 7 September 2019
(This article belongs to the Special Issue Graph Partitioning: Theory, Engineering, and Applications)
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. View Full-Text
Keywords: density matrix; G-SP2; graph partitioning; molecular dynamics; QMD; SP2 algorithm density matrix; G-SP2; graph partitioning; molecular dynamics; QMD; SP2 algorithm
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Djidjev, H.N.; Hahn, G.; Mniszewski, S.M.; Negre, C.F.A.; Niklasson, A.M.N. Using Graph Partitioning for Scalable Distributed Quantum Molecular Dynamics. Algorithms 2019, 12, 187.

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