Verlet-I/r-RESPA/Impulse is limited by nonlinear instabilities

SIAM Journal on Scientific Computing

Volumn 24, Issue 6, 2003, Pages 1951-1973

  Ma, Qun ^a   Izaguirre, Jesús A ^a   Skeel, Robert D ^b  

^a 236 Hesburgh Center for International Studies   (United States)

^b UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

KAM theory; Langevin stabilization; Long molecular dynamics simulations; Mollified impulse method; Multiple time stepping; Nonlinear instability; Verlet I r RESPA Impulse

Indexed keywords

ASYMPTOTIC STABILITY; COMPUTER SIMULATION; DROP FORMATION; INTEGRATION; MATHEMATICAL MODELS; MATRIX ALGEBRA; MOLECULAR DYNAMICS; ORDINARY DIFFERENTIAL EQUATIONS; PERTURBATION TECHNIQUES; PROTEINS; VECTORS; WATER;

LANGEVIN STABILIZATION; LONG MOLECULAR DYNAMICS SIMULATION; MOLLIFIED IMPULSE METHOD; MULTIPLE TIME STEPPING INTEGRATOR; NONLINEAR INSTABILITY;

EQUATIONS OF MOTION;

EID: 0346946971     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827501399833     Document Type: Article

References (45)

1. H. C. Andersen, Rattle: A 'velocity' version of the shake algorithm for molecular dynamics calculations, J. Comput. Phys., 52 (1983), pp. 24-34.
2. E. Barth and T. Schlick, Extrapolation versus impulse in multiple-timestepping schemes II. Linear analysis and applications to Newtonian and Langevin dynamics, J. Chem. Phys., 109 (1998), pp. 1633-1642.
3. P. F. Batcho, D. A. Case, and T. Schlick, Optimized particle-mesh Ewald/multiple-time step integration for molecular dynamics simulations, J. Chem. Phys., 115 (2001), pp. 4003-4018.
4. P. F. Batcho and T. Schlick, New splitting formulations for lattice summations, J. Chem. Phys., 115 (2001), pp. 8312-8326.
5. P. F. Batcho and T. Schlick, Special stability advantages of position-verlet over velocity-verlet in multiple-time step integration, J. Chem. Phys., 115 (2001), pp. 4019-4029.
6. H. J. C. Berendsen and W. F. van Gunsteren, Practical algorithms for dynamic simulations, in Proc. Internat. School of Phys., Enrico Fermi, 97, G. C. Ciccotti and W. G. Hoover, eds., Amsterdam, North-Holland, 1986, pp. 43-65.
7. J. J. Biesiadecki and R. D. Skeel, Dangers of multiple-time-step methods, J. Comput. Phys., 109 (1993), pp. 318-328.
8. T. Bishop, R. D. Skeel, and K. Schulten, Difficulties with multiple timestepping and the fast multipole algorithm in molecular dynamics, J. Comput. Chem., 18 (1997), pp. 1785-1791.
9. B. García-Archilla, J. M. Sanz-Serna, and R. D. Skeel, Long-time-step methods for oscillatory differential equations, SIAM J. Sci. Comput., 20 (1998), pp. 930-963.
10. B. García-Archilla, J. M. Sanz-Serna, and R. D. Skeel, The mollified impulse method for oscillatory differential equations, in Numerical Analysis, D. F. Griffiths and G. A. Watson, eds., London, Pitman, 1998, pp. 111-123.
11. M. Gribskov, L. Wesson, and D. Eisenberg, Melittin, the 2mlt protein, Structure available online from http://www.rcsb.org/pdb/ (15 October 1990).
12. H. Grubmüller, H. Heller, A. Windemuth, and K. Schulten, Generalized Verlet algorithm for efficient molecular dynamics simulations with long-range interactions, Molecular Simulation, 6 (1991), pp. 121-142.
13. E. Hairer, S. P. Nørsett, and G. Wanner, Solving Ordinary Differential Equations I: Non-stiff Systems, Springer-Verlag, Berlin, 1987.
14. D. D. Humphreys, R. A. Friesner, and B. J. Berne, A multiple-time-step molecular dynamics algorithm for macromolecules, J. Phys. Chem., 98 (1994), pp. 6885-6892.
15. J. A. Izaguirre, Longer Time Steps for Molecular Dynamics, Ph.D. thesis, University of Illinois at Urbana-Champaign, Urbana, IL, 1999.
16. J. A. Izaguirre, Generalized mollified multiple time stepping methods for molecular dynamics, in Multiscale Computational Methods in Chemistry and Physics, NATO Sci. Ser. F Comput. Syst. Sci. 177, A. Brandt, J. Bernholc, and K. Binder, eds., IOS Press, Amsterdam 2001, pp. 34-47.
17. J. A. Izaguirre, D. P. Catarello, J. M. Wozniak, and R. D. Skeel, Langevin stabilization of molecular dynamics, J. Chem. Phys., 114 (2001), pp. 2090-2098.
18. J. A. Izaguirre, Q. Ma, T. Matthey, J. Willcock, T. Slabach, B. Moore, and G. Viamontes, Overcoming instabilities in Verlet-I/r-RESPA with the mollified impulse method, in Proceedings of 3rd International Workshop on Methods for Macromolecular Modeling, Lect. Notes Comput. Sci. Eng. 24, T. Schlick and H. H. Gan, eds., Springer-Verlag, Berlin, New York, 2002, pp. 146-174.
19. T. Matthey, T. Cickovski, S. Hampton, A. Ko, Q. Ma, T. Slabach, and J. Izaguirre, PROTOMOL, an object-oriented framework for prototyping novel applications of molecular dynamics, ACM Trans. Math. Software, submitted.
20. J. A. Izaguirre, S. Reich, and R. D. Skeel, Longer time steps for molecular dynamics, J. Chem. Phys., 110 (1999), pp. 9853-9864.
21. W. L. Jorgensen, J. Chandrasekhar, J. D. Madura, R. W. Impey, and M. L. Klein, Comparison of simple potential functions for simulating liquid water, J. Chem. Phys., 79 (1983), pp. 926-935.
22. L. Kalé, R. Skeel, M. Bhandarkar, R. Brunner, A. Gursoy, N. Krawetz, J. Phillips, A. Shinozaki, K. Varadarajan, and K. Schulten, NAMD2: Greater scalability for parallel molecular dynamics, J. Comput. Phys., 151 (1999), pp. 283-312.
23. A. R. Leach, Molecular Modelling: Principles and Applications, Addison-Wesley Longman, Reading, MA, 1996.
24. T. R. Littell, R. D. Skeel, and M. Zhang, Error analysis of symplectic multiple time stepping, SIAM J. Numer. Anal., 34 (1997); pp. 1792-1807.
25. Q. Ma and J. A. Izaguirre, Targeted mollified Impulse - A multiscale stochastic integrator for molecular dynamics, Multiscale Model. Simul., submitted.
26. Q. Ma and J. A. Izaguirre, Long time step molecular dynamics using targeted Langevin stabilization, in Proceedings of the ACM Symposium on Applied Computing, Melbourne, FL, 2003, pp. 178-182
27. A. D. MacKerell Jr., D. Bashford, M. Bellott, R. L. Dunbrack Jr., J. Evanseck, M. J. Field, S. Fischer, J. Gao, S. Ha, D. Joseph, L. Kuchnir, K. Kuczera, F.T. K. Lau, C. Mattos, S. Michnick, T. Ngo, D. T. Nguyen, B. Prodhom, I. W. E. Reiher, B. Roux, M. Schlenkrich, J. Smith, R. Stote, J. Straub, M. Watanabe, J. Wiorkiewicz-Kuczera, D. Yin, and M. Karplus, All-hydrogen empirical potential for molecular modeling and dynamics studies of proteins using the CHARMM22 force field, J. Phys. Chem. B, 102 (1998), pp. 3586-3616.
28. A. D. MacKerell Jr., D. Bashford, M. Bellott, R. L. Dunbrack Jr., J. Evanseck, M. J. Field, S. Fischer, J. Gao, H. Guo, S. Ha, D. Joseph, L. Kuchnir, K. Kuczera, F. T. K. Lau, C. Mattos, S. Michnick, T. Ngo, D. T. Nguyen, B. Prodhom, B. Roux, M. Schlenkrich, J. Smith, R. Stote, J. Straub, M. Watanabe, J. Wiorkiewicz-Kuczera, D. Yin, and M. Karplus, Self-consistent parameterization of biomolecules for molecular modeling and condensed phase simulations, FASEB J., p. 6:A143, 1992.
29. M. Mandziuk and T. Schlick, Resonance in the dynamics of chemical systems simulated by the implicit midpoint scheme, Chem. Phys. Lett., 237 (1995), pp. 525-535.
30. T. Matthey and J. A. Izaguirre, ProtoMol: A molecular dynamics framework with incremental parallelization, in Proceedings of the Tenth SIAM Conference on Parallel Processing for Scientific Computing, Portsmouth, VA, 2001, CD-ROM, SIAM, Philadelphia, PA, 2001.
31. S. Miyamoto and P. A. Kollman, Settle: An analytical version of the Shake and Rattle algorithm for rigid water molecules, J. Comput. Chem., 13 (1992), pp. 952-962.
32. P. Procacci, personal communication, 2002.
33. P. Procacci and M. Marchi, Taming the Ewald sum in molecular dynamics simulations of solvated proteins via a multiple time step algorithm, J. Chem. Phys., 104 (1996), pp. 3003-3012.
34. P. Procacci, M. Marchi, and G. J. Martyna, Electrostatic calculations and multiple time scales in molecular dynamics simulation of flexible molecular systems, J. Chem. Phys., 108 (1998), pp. 8799-8803.
35. R. D. Skeel and K. Srinivas, Nonlinear stability analysis of area-preserving integrators, SIAM J. Numer. Anal., 38 (2000), pp. 129-148.
36. A. Sandu and T. Schlick, Masking resonance artifacts in force-splitting methods for biomolecular simulations by extrapolative Langevin dynamics, J. Comput. Phys, 151 (1999), pp. 74-113.
37. J. M. Sanz-Serna and M. P. Calvo, Numerical Hamiltonian Problems, Chapman and Hall, London, 1994.
38. T. Schlick, M. Mandziuk, R. D. Skeel, and K. Srinivas, Nonlinear resonance artifacts in molecular dynamics simulations, J. Comput. Phys., 139 (1998), pp. 1-29.
39. R. D. Skeel, Integration schemes for molecular dynamics and related applications, in The Graduate Student's Guide to Numerical Analysis, Springer Ser. Comput. Math. 26, M. Ainsworth, J. Levesley, and M. Marletta, eds., Springer-Verlag, Berlin, 1999, pp. 119-176.
40. R. D. Skeel and J. A. Izaguirre, The five femtosecond time step barrier, in Computational Molecular Dynamics: Challenges, Methods, Ideas, Lect. Notes Comput. Sci. Eng. 4, P. Deuflhard, J. Hermans, B. Leimkuhler, A. Mark, S. Reich, and R. D. Skeel, eds., Springer-Verlag, Berlin-Heidelberg-New York, 1998, pp. 303-318.
41. R. D. Skeel, G. Zhang, and T. Schlick, A family of symplectic integrators: Stability, accuracy, and molecular dynamics applications, SIAM J. Sci. Comput., 18 (1997), pp. 203-222.
42. M. Tuckerman, B. J. Berne, and G. J. Martyna, Reversible multiple time scale molecular dynamics, J. Chem. Phys., 97 (1992), pp. 1990-2001.
43. W. F. van Gunsteren and H. J. C. Berendsen, Algorithms for macromolecular dynamics and constraint dynamics, Mol. Phys., 34 (1977), pp. 1311-1327.
44. R. Zhou and B. J. Berne, A new molecular dynamics method combining the reference system propagator algorithm with a fast multipole method for simulating proteins and other complex systems, J. Chem. Phys., 103 (1995), pp. 9444-9459.
45. R. Zhou, E. Harder, H. Xu, and B. J. Berne, Efficient multiple time step method for use with ewald and particle mesh ewald for large biomolecular systems, J. Chem. Phys., 115 (2001), pp. 2348-2358.