Abstract
Recent results on supercomputers show that beyond 65 K cores, the efficiency of molecular dynamics simulations of interfacial systems decreases significantly. In this paper, we introduce a dynamic cutoff method (DCM) for interfacial systems of arbitrarily large size. The idea consists in adopting a cutoff-based method in which the cutoff is chosen on a particle-by-particle basis, according to the distance from the interface. Computationally, the challenge is shifted from the long-range solvers to the detection of the interfaces and to the computation of the particle-interface distances. For these tasks, we present linear-time algorithms that do not rely on global communication patterns. As a result, the DCM algorithm is suited for large systems of particles and massively parallel computers. To demonstrate its potential, we integrated DCM into the LAMMPS open-source molecular dynamics package, and simulated large liquid/vapor systems on two supercomputers: SuperMuc and JUQUEEN. In all cases, the accuracy of DCM is comparable to the traditional particle-particle particle-mesh (PPPM) algorithm, while the performance is considerably superior for large numbers of particles. For JUQUEEN, we provide timings for simulations running on the full system (458, 752 cores), and show nearly perfect strong and weak scaling.
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Notes
- 1.
With the exception of a reduction operation to identify the maximum of a scalar in the interface detection method.
- 2.
The edge length h determines the resolution of the interface and can be automatically chosen at the beginning of the simulation.
- 3.
\(D^p = \{ d_{x,y,z} \in \mathbb {R}\,|\, 0 \le x < N_x, 0 \le y < N_y, 0 \le z < N_z\}\); the superscript p indicates that this set is computed on each process, in parallel.
- 4.
The exact value for the threshold is not important here. More information is provided in [25].
- 5.
Possible interpolation functions and the resulting accuracy are discussed in [25].
- 6.
If a body i exerts a force f onto another body j, then j exerts a force \(-f\) on i.
- 7.
This is why most GPU implementations of force calculations also neglect N3.
- 8.
Running on 1024 cores on the BlueGene/Q supercomputer with simultaneous multi-threading enabled for four threads per core.
- 9.
\(f_{i_z}^*\) is computed by the accurate (but expensive) Ewald long-range solver.
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Acknowledgments
The authors gratefully acknowledge financial support from the Deutsche Forschungsgemeinschaft (German Research Association) through grant GSC 111, computing resources on the supercomputer JUQUEEN at Jülich Supercomputing Centre (JSC) (project ID: e5430301) and the Gauss Centre for Supercomputing/Leibniz Supercomputing Centre (project ID: pr84za), and Edoardo Di Napoli and Benjamin Berkels for helpful discussions.
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Springer, P., Ismail, A.E., Bientinesi, P. (2015). A Scalable, Linear-Time Dynamic Cutoff Algorithm for Molecular Dynamics. In: Kunkel, J., Ludwig, T. (eds) High Performance Computing. ISC High Performance 2015. Lecture Notes in Computer Science(), vol 9137. Springer, Cham. https://doi.org/10.1007/978-3-319-20119-1_12
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