Scalability and Performance of a Program that Uses Domain Decomposition for Monte Carlo Simulation of Molecular Liquids

Authors

  • Alexander V. Teplukhin Institute of Mathematical Problems of Biology of RAS - the Branch of Keldysh Institute of Applied Mathematics of RAS, Pushchino, Russian Federation https://orcid.org/0000-0002-3285-0240

DOI:

https://doi.org/10.14529/jsfi220303

Keywords:

parallel calculation, biopolymers, Monte Carlo, MPI

Abstract

The main factors hindering the development of supercomputer programs for molecular simulation by the Monte Carlo method within the framework of classical physics are considered, and possible ways to eliminate the problems that arise in this case are discussed. Thus, the use of molecular models with moderate stiffness of covalent bonds between fragments makes it possible not only to increase the efficiency of scanning the configuration space of the model, but also to abandon the complex apparatus of kinematics with rigid links, which significantly limits the possibilities of domain decomposition. Based on the domain decomposition strategy and a simplified treatment of the deformation energy of covalent bonds and angles, an original parallel algorithm for calculating the properties of large all-atomic models of aqueous solutions of biopolymers by the Monte Carlo method was developed. To speed up computations within the framework of this approach, each domain is assigned its own group of processors/cores using local data replication and splitting the loop over the interacting partners. The article discusses the logical scheme of the computational algorithm and the main components of the software package (fortran77, MPI 1.2). Test calculations performed for water and n-hexane demonstrated the high performance and scalability of the program in which the proposed algorithm was implemented.

References

Allen, F.H., Kennard, O., Watson, D.G., et al.: Tables of bond lengths determined by X-ray and neutron diffraction. Part 1. Bond lengths in organic compounds. J. Chem. Soc., Perkin Trans. 2 pp. S1–S19 (1987). https://doi.org/10.1039/P298700000S1

Allen, M.P., Tildesley, D.J.: Computer Simulation of Liquids. Cambridge University Press, New York (1987)

Anderson, J.A., Jankowski, E., Grubbb, T.L., et al.: Massively parallel Monte Carlo for many-particle simulations on GPUs. J. Comput. Phys. 254, 27–38 (2013). https://doi.org/10.1016/j.jcp.2013.07.023

Berendsen, H.J.C., Grigera, J.R., Straatsma, T.P.: The missing term in effective pair potentials. J. Phys. Chem. 91, 6269–6271 (1987). https://doi.org/10.1021/j100308a038

Cornell, W.D., Cieplak, P., Bayly, C.I., et al.: A second generation force field for the simulation of proteins, nucleic acids, and organic molecules. J. Am. Chem. Soc. 117, 5179–5197 (1995). https://doi.org/10.1021/ja00124a002

Dubbeldam, D., Torres-Knoop, A., Walton, K.S.: On the inner workings of Monte Carlo codes. Mol. Simul. 39, 1253–1292 (2013). https://doi.org/10.1080/08927022.2013.819102

Durstenfeld, R.: Algorithm 235: Random permutation. Commun. ACM 7, 420 (1964). https://doi.org/10.1145/364520.364540

Gō, N., Scheraga, H.A.: Analysis of the contribution of internal vibrations to the statistical weights of equilibrium conformations of macromolecules. J. Chem. Phys. 51, 4751–4767 (1969). https://doi.org/10.1063/1.1671863

Hammersley, J.M., Handscomb, D.C.: Monte Carlo Methods. Methuen, London (1964)

Heffelfinger, G.S., Lewitt, M.E.: A comparison between two massively parallel algorithms for Monte Carlo computer simulation: An investigation in the grand canonical ensemble. J. Comput. Chem. 17, 250–265 (1996). https://doi.org/10.1002/(SICI)1096-987X(19960130)17:2<250::AID-JCC11>3.0.CO;2-N

Jorgensen, W.L., Maxwell, D.S., Tirado-Rives, J.: Development and testing of the OPLS all-atom force field on conformational energetics and properties of organic liquids. J. Am. Chem. Soc. 118, 11225–11236 (1996). https://doi.org/10.1021/ja9621760

Jorgensen, W.L., Tirado-Rives, J.: Monte Carlo vs molecular dynamics for conformational sampling. J. Phys. Chem. 100, 14508–14513 (1996). https://doi.org/10.1021/jp960880x

Kalos, M.H., Whitlock, P.A.: Monte Carlo Methods. Wiley-VCH, Weinheim (2008)

Kalugin, M.D., Teplukhin, A.V.: Study of caffeineDNA interaction in aqueous solution by parallel Monte Carlo simulation. J. Struct. Chem. 50, 841–852 (2009). https://doi.org/10.1007/s10947-009-0126-8

Kumar, S., Huang, C., Zheng, G., et al.: Scalable molecular dynamics with NAMD on the IBM Blue Gene/L system. IBM Journal of Research and Development 52(1-2), 177–188 (2008). https://doi.org/10.1147/rd.521.0177

Landau, D.P., Binder, K.: A Guide to Monte Carlo Simulations in Statistical Physics. Cambridge University Press, New York (2000)

Mavrantzas, V.G.: Using Monte Carlo to simulate complex polymer systems: Recent progress and outlook. Front. Phys. 9, 661367 (2021). https://doi.org/10.3389/fphy.2021.661367

Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., et al.: Equation of state calculations by fast computing machines. J. Chem. Phys. 21, 1087–1092 (1953). https://doi.org/10.1063/1.1699114

Metropolis, N., Ulam, S.: The Monte Carlo method. J. Am. Statist. Assoc. 44, 335–341 (1949). https://doi.org/10.1080/01621459.1949.10483310

Northrup, S.A., McCammon, J.A.: Simulation methods for protein structure fluctuations. Biopolymers 19, 1001–1016 (1980). https://doi.org/10.1002/bip.1980.360190506

Pawley, G.S., Bowler, K.C., Kenway, R.D., Wallace, D.J.: Concurrency and parallelism in MC and MD simulations in physics. Comput. Phys. Comm. 37, 251–260 (1985). https://doi.org/10.1016/0010-4655(85)90160-2

Plimpton, S.: Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117, 1–19 (1995). https://doi.org/10.1006/jcph.1995.1039

Preis, T., Virnau, P., Paul, W., Schneider, J.J.: GPU accelerated Monte Carlo simulation of the 2D and 3D Ising model. J. Comput. Phys. 228, 4468–4477 (2009). https://doi.org/10.1016/j.jcp.2009.03.018

Rader, A.J.: Coarse-grained models: Getting more with less. Curr. Opin. Pharmacol. 10, 753–759 (2010). https://doi.org/10.1016/j.coph.2010.09.003

Teplukhin, A.V.: Multiprocessor simulation of mesoscopic DNA fragments hydration. Matem. Model. 16(11), 15–24 (2004), http://www.mathnet.ru/links/037077e2238f8f9887f8fa8da9fae408/mm219.pdf

Teplukhin, A.V.: Parallel and distributed computing in problems of supercomputer simulation of molecular liquids by the Monte Carlo method. J. Struct. Chem. 54, 65–74 (2013). https://doi.org/10.1134/S0022476613010095

Teplukhin, A.V.: A simplified treatment of the deformations of covalent bonds and angles during the all-atom Monte Carlo simulation of polymers. Polym. Sci., ser. C 55, 103–111 (2013). https://doi.org/10.1134/S1811238213050044

Teplukhin, A.V.: Short-range potential functions in computer simulations of water and aqueous solutions. J. Struct. Chem. 57, 1627–1654 (2016). https://doi.org/10.1134/S0022476616080205

Teplukhin, A.V.: Monte Carlo simulation of the local ordering of water molecules. II. Spatial correlations and hydrogen bonds. J. Struct. Chem. 59, 1624–1630 (2018). https://doi.org/10.1134/S0022476618070144

Teplukhin, A.V.: Thermodynamic and structural characteristics of SPC/E water at 290 K and under high pressure. J. Struct. Chem. 60, 1590–1598 (2019). https://doi.org/10.1134/S0022476619100044

Teplukhin, A.V.: Monte Carlo calculation of thermodynamic and structural characteristics of liquid hydrocarbons. J. Struct. Chem. 62, 7082 (2021). https://doi.org/10.1134/S002247662101008X

Teplukhin, A.V.: Parametrization of the torsion potential in all-atom models of hydrocarbon molecules using a simplified expression for the deformation energy of valence bonds and angles. J. Struct. Chem. 62, 1653–1666 (2021). https://doi.org/10.1134/S0022476621110019

Uhlherr, A., Leak, S.J., Adam, N.E., et al.: Large scale atomistic polymer simulations using Monte Carlo methods for parallel vector processors. Comput. Phys. Comm. 144, 1–22 (2002). https://doi.org/10.1016/S0010-4655(01)00464-7

Vitalis, A., Pappu, R.V.: Methods for Monte Carlo simulations of biomacromolecules. Annu. Rep. Comput. Chem. 5, 49–76 (2009). https://doi.org/10.1016/S1574-1400(09)-00503-9

Wichmann, B.A., Hill, I.D.: Generating good pseudo-random numbers. Comput. Statist. Data Anal. 51, 1614–1622 (2006). https://doi.org/10.1016/j.csda.2006.05.019

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Published

2022-11-30

How to Cite

Teplukhin, A. V. (2022). Scalability and Performance of a Program that Uses Domain Decomposition for Monte Carlo Simulation of Molecular Liquids. Supercomputing Frontiers and Innovations, 9(3), 51–64. https://doi.org/10.14529/jsfi220303