A Scalable, Linear-Time Dynamic Cutoff Algorithm for Molecular Dynamics

  • Paul Springer
  • Ahmed E. Ismail
  • Paolo Bientinesi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9137)

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.

Keywords

Dynamic cutoff Interface detection Linear-time complexity Scalability Molecular dynamics Fast sweeping method 

References

  1. 1.
    Berkels, B.: An unconstrained multiphase thresholding approach for image segmentation. In: Tai, X.-C., Mørken, K., Lysaker, M., Lie, K.-A. (eds.) SSVM 2009. LNCS, vol. 5567, pp. 26–37. Springer, Heidelberg (2009) CrossRefGoogle Scholar
  2. 2.
    Blokhuis, E., Bedeaux, D., Holcomb, C., Zollweg, J.: Tail corrections to the surface tension of a lennard-jones liquid-vapour interface. Mol. Phys. 85(3), 665–669 (1995)CrossRefGoogle Scholar
  3. 3.
    Bohlen, T.: Parallel 3-d viscoelastic finite difference seismic modelling. Comput. Geosci. 28(8), 887–899 (2002)CrossRefGoogle Scholar
  4. 4.
    Bradley, R., Radhakrishnan, R.: Coarse-grained models for protein-cell membrane interactions. Polymers 5(3), 890–936 (2013)CrossRefGoogle Scholar
  5. 5.
    Bresme, F., Chacón, E., Tarazona, P.: Molecular dynamics investigation of the intrinsic structure of water-fluid interfaces via the intrinsic sampling method. Phys. Chem. Chem. Phys. 10(32), 4704–4715 (2008)CrossRefGoogle Scholar
  6. 6.
    Chapela, G.A., Saville, G., Thompson, S.M., Rowlinson, J.S.: Computer simulation of a gas-liquid surface. Part 1. J. Chem. Soc. Faraday Trans. 2: Mol. Chem. Phys. 73(7), 1133–1144 (1977)CrossRefGoogle Scholar
  7. 7.
    Chialvo, A.A., Debenedetti, P.G.: On the use of the verlet neighbor list in molecular dynamics. Comput. Phys. Commun. 60(2), 215–224 (1990)CrossRefGoogle Scholar
  8. 8.
    Ewald, P.: Die berechnung optischer und elektrostatischer gitterpotentiale. Annalen der Physik 369, 253–287 (1921)CrossRefGoogle Scholar
  9. 9.
    Griebel, M., Knapek, S., Zumbusch, G.: Numerical Simulation in Molecular Dynamics. Springer, Heidelberg (2007) MATHGoogle Scholar
  10. 10.
    Guo, M., Peng, D.-Y., Lu, B.C.-Y.: On the long-range corrections to computer simulation results for the Lennard-Jones vapor-liquid interface. Fluid Phase Equilib. 130(1), 19–30 (1997)CrossRefGoogle Scholar
  11. 11.
    Hill, T.L.: Thermodynamics of Small Systems. Dover Publications, Mineola (2013)Google Scholar
  12. 12.
    Hockney, R., Goel, S., Eastwood, J.: Quiet high-resolution computer models of a plasma. J. Comput. Phys. 14(2), 148–158 (1974)CrossRefGoogle Scholar
  13. 13.
    in ’t Veld, P.J., Ismail, A.E., Grest, G.S.: Application of ewald summations to long-range dispersion forces. J. Chem. Phys. 127, 144711 (2007)CrossRefGoogle Scholar
  14. 14.
    Isele-Holder, R.E., Ismail, A.E.: Atomistic potentials for trisiloxane, alkyl ethoxylate, and perfluoroalkane-based surfactants with tip4p/2005 and application to simulations at the airwater interface. J. Phys. Chem. B 118(31), 9284–9297 (2014)CrossRefGoogle Scholar
  15. 15.
    Isele-Holder, R.E., Mitchell, W., Hammond, J.R., Kohlmeyer, A., Ismail, A.E.: Reconsidering dispersion potentials: reduced cutoffs in mesh-based ewald solvers can be faster than truncation. J. Chem. Theory Comput. 9(12), 5412–5420 (2013)CrossRefGoogle Scholar
  16. 16.
    Isele-Holder, R.E., Mitchell, W., Ismail, A.E.: Development and application of a particle-particle particle-mesh ewald method for dispersion interactions. J. Chem. Phys. 137(17), 174107 (2012)CrossRefGoogle Scholar
  17. 17.
    Ismail, A.E., Tsige, M., in ’t Veld, P.J., Grest, G.S.: Surface tension of normal and branched alkanes. Mol. Phys. 105(23–24), 3155–3163 (2007)CrossRefGoogle Scholar
  18. 18.
    Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. Commun. Pure Appl. Math. 42(5), 577–685 (1989)MATHMathSciNetCrossRefGoogle Scholar
  19. 19.
    Pártay, L.B., Hantal, G., Jedlovszky, P., Vincze, Á., Horvai, G.: A new method for determining the interfacial molecules and characterizing the surface roughness in computer simulations. Application to the liquid-vapor interface of water. J. Comput. Chem. 29(6), 945–956 (2008)CrossRefGoogle Scholar
  20. 20.
    Plimpton, S.: Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117(1), 1–19 (1995)MATHCrossRefGoogle Scholar
  21. 21.
    Rumpf, A.G.: Quocmesh software library. Institute for Numerical Simulation, University of Bonn. http://numod.ins.uni-bonn.de/software/quocmesh/
  22. 22.
    Sega, M., Kantorovich, S.S., Jedlovszky, P., Jorge, M.: The generalized identification of truly interfacial molecules (ITIM) algorithm for nonplanar interfaces. J. Chem. Phys. 138(4), 044110 (2013)CrossRefGoogle Scholar
  23. 23.
    Sethian, J.A.: A fast marching level set method for monotonically advancing fronts. Proc. Nat. Acad. Sci. 93(4), 1591–1595 (1996)MATHMathSciNetCrossRefGoogle Scholar
  24. 24.
    Shekhar, A., Nomura, K.-I., Kalia, R.K., Nakano, A., Vashishta, P.: Nanobubble collapse on a silica surface in water: Billion-atom reactive molecular dynamics simulations. Phys. Rev. Lett. 111, 184503 (2013)CrossRefGoogle Scholar
  25. 25.
    Springer, P.: A scalable, linear-time dynamic cutoff algorithm for molecular simulations of interfacial systems (2013). arXiv:1502.0323
  26. 26.
    Sun, Y., Zheng, G., Mei, C., Bohm, E.J., Phillips, J.C., Kalé, L.V., Jones, T.R.: Optimizing fine-grained communication in a biomolecular simulation application on cray xk6. In: 2012 International Conference on High Performance Computing, Networking, Storage and Analysis (SC), pp. 1–11. IEEE (2012)Google Scholar
  27. 27.
    Tameling, D., Springer, P., Bientinesi, P., Ismail, A.E.: Multilevel summation for dispersion: a linear-time algorithm for \(r^{-6}\) potentials. J. Chem. Phys. 140(2), 024105 (2014)CrossRefGoogle Scholar
  28. 28.
    Verlet, L.: Computer “experiments" on classical fluids. I. thermodynamical properties of Lennard-Jones molecules. Phys. Rev. 159, 98–103 (1967)CrossRefGoogle Scholar
  29. 29.
    Wang, H., Schütte, C., Zhang, P.: Error estimate of short-range force calculation in inhomogeneous molecular systems. Phys. Rev. E 86(2), 026704 (2012)CrossRefGoogle Scholar
  30. 30.
    Wennberg, C.L., Murtola, T., Hess, B., Lindahl, E.: Lennard-Jones lattice summation in bilayer simulations has critical effects on surface tension and lipid properties. J. Chem. Theory Comput. 9, 3527–3537 (2013)CrossRefGoogle Scholar
  31. 31.
    Zhao, H.: Parallel implementations of the fast sweeping method. J. Comput. Math. 25(4), 421–429 (2007)MathSciNetGoogle Scholar
  32. 32.
    Zhao, H.-K., Osher, S., Merriman, B., Kang, M.: Implicit and nonparametric shape reconstruction from unorganized data using a variational level set method. Comput. Vis. Image Underst. 80(3), 295–314 (2000)MATHCrossRefGoogle Scholar
  33. 33.
    Zubillaga, R.A., Labastida, A., Cruz, B., Martínez, J.C., Sánchez, E., Alejandre, J.: Surface tension of organic liquids using the OPLS/AA force field. J. Chem. Theory Comput. 9, 1611–1615 (2013)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Paul Springer
    • 1
  • Ahmed E. Ismail
    • 1
  • Paolo Bientinesi
    • 1
  1. 1.Aachen Institute for Advanced Study in Computational Engineering ScienceRWTH Aachen UniversityAachenGermany

Personalised recommendations