Error and timing analysis of multiple time-step integration methods for molecular dynamics

Computer Physics Communications

Volumn 176, Issue 4, 2007, Pages 271-291

  Han, Guowen ^a   Deng, Yuefan ^a,b   Glimm, James ^a   Martyna, Glenn ^c  

^a Stony Brook University   (United States)

^b NANKAI UNIVERSITY   (China)

^c IBM T J WATSON RESEARCH CENTER   (United States)

Author keywords

Coulomb forces; Error analysis; Ewald methods; Molecular dynamics; Multiple time step

Indexed keywords

CONSTRAINT THEORY; ERROR ANALYSIS; INTEGRATION; LINEAR SYSTEMS; MOLECULAR VIBRATIONS; TIME SERIES ANALYSIS;

COULOMB FORCES; EWALD METHODS; MULTIPLE TIME-STEPS; TIMING ANALYSIS;

MOLECULAR DYNAMICS;

EID: 33846386224     PISSN: 00104655     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cpc.2006.10.005     Document Type: Article

References (49)

1. Allen M.P., and Tildesley D.J. Computer Simulation of Liquids (1987), Clarendon, Oxford
2. Andersen H.C. Rattle: A "velocity" version of the shake algorithm for molecular dynamics calculations. J. Comp. Phys. 52 (1983) 24
3. Barash D., Yang L., Qian X., and Schlick T. Inherent speedup limitations in multiple time step/particle mesh Ewald algorithms. J. Comp. Chem. 24 (2003) 77
4. Barth E., and Schlick T. Overcoming stability limitations in biomolecular dynamics. I. Combining force splitting via extrapolation with Langevin dynamics in LN. J. Chem. Phys. 109 (1998) 1617
5. Barth E., and Schlick T. Extrapolation versus impulse in multiple-timestepping schemes. II. Linear analysis and applications to Newtonian and Langevin dynamics. J. Chem. Phys. 109 (1998) 1633
6. Biesiadecki J.J., and Skeel R.D. Dangers of multiple time step methods. J. Comp. Phys. 109 (1993) 318
7. Bishop T.C., Skeel R.K., and Schulten K. Difficulties with multiple time stepping and fast multipole algorithm in molecular dynamics. J. Comp. Chem. 18 (1997) 1785
8. Chin S.A. Dynamical multiple-time stepping methods for overcoming resonance instabilities. J. Chem. Phys. 120 (2004) 8
9. Darden T.A., York D.M., and Pedersen L.G. Particle mesh Ewald: An N log (N) method for Ewald sums in large systems. J. Chem. Phys. 98 (1993) 10089
10. Deng Y., Glimm J., Davenport J.W., Cai X., and Santos E. Performance models on QCDOC for molecular dynamics with Coulomb potentials. J. High Perform. Comp. Appl. 18 (2004) 183
11. Ewald P.P. Die Berechnung optischer und elektrostatischer Gitterpotentiale. Ann. Phys. 64 (1921) 253
12. Fitch B.G., Germain R.S., Mendell M., Pitera J., Pitman M., Rayshubskiy A., Sham Y., Suits F., Swope W., Wald T.J.C., ZhestKov Y., and Zhou R. Blue Matter, an application framework for molecular simulation on Blue Gene. J. Parallel Distrib. Comput. 63 (2003) 759
13. Forester T., and Smith W. On multiple time-step algorithms and the Ewald sum. Mol. Sim. 13 (1994) 195
14. Gibbon P., and Sutmann G. Long-range interactions in many-particle simulation. In: Grotendorst J., Marx D., and Muramatsu A. (Eds). Quantum Simulations of Complex Many-Body Systems: From Theory to Algorithms. Lecture Notes, NIC Series vol. 10 (2002), John von Neumann Institute for Computing, Jülich 467-506
15. Greengard L. The Rapid Evaluation of Potential Fields in Particle Systems (1988), MIT Press, Cambridge, MA
16. Grubmüller H., Heller H., Windemuth A., and Schulten K. Generalized Verlet algorithm for efficient molecular dynamics simulations with long-range interactions. Mol. Sim. 6 (1991) 121-142
17. Grubmüller H., and Tavan P. Multiple time step algorithms for MD simulations of proteins: How good are they?. J. Comp. Chem. 19 (1998) 1534
18. Hayli A. Le problème des N corps dans un champ extérieur application a l'évolution dynamique des amas ouverts-I. Bull. Astronomique 2 (1967) 67
19. Hockney R.W., and Eastwood J.W. Computer Simulations Using Particles (1988), IOP, Bristol
20. Humphreys D.D., Friesner R.A., and Berne B.J. A multiple-time-step molecular dynamics algorithm for macromolecules. J. Phys. Chem. 98 (1994) 6885
21. Izaguirre J.A., Reich S., and Skeel R.D. Longer time steps for molecular dynamics. J. Chem. Phys. 110 (1999) 9853
22. Kolafa J., and Perram J.W. Cutoff errors in the Ewald summation formulae for point charge system. Mol. Sim. 9 (1992) 351
23. Minary P., Tuckerman M.E., and Martyna G.J. Long time molecular dynamics for enhanced sampling of biomolecular systems. Phys. Rev. Lett. 93 (2004) 150201
24. Miyamoto S., and Kollman P.A. SETTLE: An analytical version of the SHAKE and RATTLE algorithm for rigid water models. J. Comp. Chem. 13 (1992) 952
25. Perram J.W., Petersen H.G., and de Leeuw S.W. An algorithm for the simulation of condensed matter which grows as the 3/2 power of the number of particles. Mol. Phys. 65 (1988) 875
26. Pollock E., and Glosli J. Comments on P3M, FMM, and the Ewald method for large periodic systems. Comput. Phys. Comm. 95 (1996) 10089
27. Procacci P., and Marchi M. Taming the Ewald sum in molecular dynamics simulations of solvated proteins via a multiple time step algorithm. J. Chem. Phys. 104 (1996) 3003
28. Procacci P., Marchi M., and Martyna G.J. Electrostatic calculations and multiple time scales in molecular dynamics simulations of flexible molecular systems. J. Phys. Chem. 108 (1998) 8799
29. Qian X., and Schlick T. Efficient multiple-time-step integrators with distance-based force splitting for particle-mesh-Ewald molecular dynamics simulations. J. Chem. Phys. 116 (2002) 5971
30. P. Rissland, Y. Deng, Structure and performance of molecular dynamics package MDoc on QCDOC, Parallel Comput., submitted for publication
31. Ryckaert J.P., Ciccotti G., and Berendsen H.J.C. Numerical integration of the Cartesian equations of motion of a system with constraints: Molecular dynamics of n-alkanes. J. Comp. Phys. 23 (1977) 327
32. Sandu A., and Schlick T. Masking resonance artifacts in force-splitting methods for biomolecular simulations by extrapolative Langevin dynamics. J. Comp. Phys. 151 (1999) 74
33. Sangster M.J.L., and Dixon M. Interionic potentials in alkali halides and their use in simulations of the molten salts. Adv. Phys. 25 (1976) 247
34. Sagui C., and Darden T.A. Molecular dynamics simulations of biomolecules: Long-range electrostatic effects. Annu. Rev. Biophys. Biomol. Struct. 28 (1999) 155
35. Sanz-Serna J., and Calvo M. Numerical Hamiltonian Problems (1994), Chapman and Hall, London
36. Schlick T. Time-trimming tricks for dynamic simulations: Splitting force updates to reduce computational work. Structure 9 (2001) R45
37. Schlick T., Barth E., and Mandziuk M. Biomolecular dynamics at long timesteps: Bridging the timescale gap between simulation and experiment. Annu. Rev. Biophys. Biomol. Struct. 26 (1997) 181
38. Schlick T., Skeel R.D., Brunger A.T., Kale L.V., Board Jr. J.A., Hermans J., and Schulten K. Algorithmic challenges in computational molecular biophysics. J. Comp. Phys. 151 (1999) 9
39. Schreiber H., and Steinhauser O. Cutoff size does strongly influence molecular dynamics results on solvated polypeptides. Biochem. 31 (1992) 5856
40. Streett W.B., Tildesley D., and Saville G. Multiple time step methods in molecular dynamics. Mol. Phys. 35 (1978) 639
41. Stuart S.J., Zhou R., and Berne B.J. Molecular dynamics with multiple time scales: The selection of efficient reference system propagators. J. Chem. Phys. 105 (1996) 1426
42. Toukmaji A., and Board J.A. Ewald sum techniques in perspective: a survey. Comput. Phys. Comm. 95 (1996) 78
43. Tuckerman M.E., Berne B.J., and Martyna G.J. Reversible multiple time scale molecular dynamics. J. Chem. Phys. 97 (1992) 1990
44. Tuckerman M.E., Martyna G.J., and Berne B.J. Molecular dynamics algorithm for multiple time scales: Systems with long range forces. J. Chem. Phys. 94 (1991) 6811
45. Watanabe M., and Karplus M. Dynamics of molecules with internal degrees of freedom by multiple time-step methods. J. Chem. Phys. 99 (1993) 8063
46. Watanabe M., and Karplus M. Simulations of macromolecules by multiple time-step methods. J. Phys. Chem. 99 (1995) 5680
47. York D.M., Darden T.A., and Pedersen L.G. The effect of long-range electrostatic interactions in simulations of macromolecular crystals: A comparison of the Ewald and truncated list methods. J. Chem. Phys. 99 (1993) 8345
48. York D.M., Yang W., Darden T.A., and Pedersen L.G. Towards the accurate modeling of DNA: the importance of long-range electrostatics. J. Amer. Chem. Soc. 117 (1995) 5001
49. Zhou R., Harder E., Xu H., and Berne B.J. Efficient multiple time step method for use with Ewald and particle mesh Ewald for large biomolecular systems. J. Chem. Phys. 115 (2001) 2348