Graph Partitioning Methods for Fast Parallel Quantum Molecular Dynamics

TL;DR

This paper explores graph partitioning techniques to enable efficient parallel computation of matrix polynomials in quantum molecular dynamics simulations, aiming to improve computational speed and scalability.

Contribution

It introduces a novel graph partitioning approach tailored for parallelizing matrix polynomial evaluations in quantum molecular dynamics, with rigorous definitions and experimental evaluation.

Findings

Partitioning quality varies across algorithms.

Parallelization reduces computation time significantly.

Effective graph partitioning improves simulation scalability.

Abstract

We study a graph partitioning problem motivated by the simulation of the physical movement of multi-body systems on an atomistic level, where the forces are calculated from a quantum mechanical description of the electrons. Several advanced algorithms have been published in the literature for such simulations that are based on evaluations of matrix polynomials. We aim at efficiently parallelizing these computations by using a special type of graph partitioning. For this, we represent the zero-nonzero structure of a thresholded matrix as a graph and partition that graph into several components. The matrix polynomial is then evaluated for each separate submatrix corresponding to the subgraphs and the evaluated submatrix polynomials are used to assemble the final result for the full matrix polynomial. The paper provides a rigorous definition as well as a mathematical justification of this partitioning problem. We use several algorithms to compute graph partitions and experimentally evaluate their performance with respect to the quality of the partition obtained with each method and the time needed to produce it.