Geometric integrators for multiple time-scale simulation

Journal of Physics A: Mathematical and General

Volumn 39, Issue 19, 2006, Pages 5379-5403

  Jia, Zhidong ^a   Leimkuhler, Ben ^b  

^a INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

^b UNIVERSITY OF LEICESTER   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33646232318     PISSN: 03054470     EISSN: 13616447     Source Type: Journal    
DOI: 10.1088/0305-4470/39/19/S04     Document Type: Article

References (35)

1. Arnold V I, Kozlov V V and Neishtadt A I 1997 Mathematical Aspects of Classical and Celestial Mechanics (Berlin: Springer)
2. Arponen T and Leimkuhler B 2004 An efficient geometric integrator for thermostatted anti-ferromagnetic models BIT 44 403-24
3. Benettin G, Galgani L and Giorgilli A 1987 Exponential law for the equilibration times among translational and vibrational degrees of freedom Phys. Lett. A 120 23-7
4. Bond S, Laird B and Leimkuhler B J 1999 The Nosé-Poincaré method for constant temperature molecular dynamics J. Comput. Phys. 151 114-34
5. Bornemann F A 1998 Homogenization in Time of Singularly Perturbed Conservative Mechanical Systems (Lecture Notes in Mathematics vol 1687) (Berlin: Springer)
6. W E and Engquist B 2003 Multiscale modeling and computation Not. AMS 50 1062-70
7. Evans D J and Morris G P 1990 Statistical Mechanics of Nonequilibrium Liquids (London: Academic)
8. Feng K 1986 Difference schemes for Hamiltonian formalism and symplectic geometry J. Comput. Math. 4 279-89
9. Garcia-Archilla B, Sanz-Serna J M and Skeel R D 1999 Long-time-step methods for oscillatory differential equations SIAM J. Sci. Comput. 20 930-63
10. Gautschi W 1961 Numerical integration of ordinary differential equations based on trigonometric polynomials Numer. Math. 3 381-97
11. Hairer E and Lubich Ch 2000 Long-time energy conservation of numerical methods for oscillatory differential equations SIAM J. Numer. Anal. 38 414-41
12. Hairer E, Lubich Ch and Wanner G 2002 Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations (Springer Series in Computational Mathematics vol 31) (Berlin: Springer)
13. Hochbruck M and Lubich Ch 1999 A Gautschi-type method for oscillatory second-order differential equations Numer. Math. 83 403-26
14. Holder T, Leimkuhler B J and Reich S 2001 Explicit variable step-size and time-reversible integration Appl. Numer. Math. 39 367-77
15. Hoover W G 1985 Canonical dynamics: equilibrium phase-space distributions Phys. Rev. A 31 1695-7
16. Huang W and Leimkuhler B J 1997 The adaptive Verlet method SIAM J. Sci. Comput. 18 239-56
17. Izaguirre J A, Reich S and Skeel R D 1999 Longer time steps for molecular dynamics J. Chem. Phys. 110 9853-64
18. Jia Z and Leimkuhler B J 2003 A parallel multiple time-scale reversible integrator for dynamics simulation J. Fut. Gen. Comput. Syst. 19 415-24
19. Jia Z and Leimkuhler B J 2005 A projective thermostatting dynamics technique SIAM J. Multi. Model. Simul. 4 563-83
20. Van Kampen N G and Oppenheim I 1986 Brownian motion as a problem of eliminating fast variables Physica A 138 231-48
21. Kolafa J 2004 Time-reversible always stable predictor-corrector method for molecular dynamics of polarizable molecules J. Comput. Chem. 25 335-42
22. Leimkuhler B 1999 Reversible adaptive regularization: perturbed Kepler motion and classical atomic trajectories R. Soc. Lond. Phil. Trans. A 357 1101-33
23. Leimkuhler B J 2002 An efficient multiple time-scale reversible integrator for the gravitational N-body problem J. Appl. Numer. Math. 43 175-90
24. Leimkuhler B J and Reich S 2001 A reversible averaging integrator for multiple time-scale dynamics J. Comput. Phys. 171 95-114
25. Leimkuhler B J and Reich S 2005 Simulating Hamiltonian Dynamics (Cambridge Monographs on Applied and Computational Mathematics) (Cambridge: Cambridge University Press)
26. Lipatov A S 2002 The Hybrid Multiscale Simulation Technology (Berlin: Springer)
27. Ma M Q and Izaguirre J 2003 Targeted mollified impulse-a multiscale stochastic integrator for long molecular dynamics simulations SIAM J. Multi. Model. Simul. 2 1-21
28. Martyna G J and Tuckerman M T 1995 Symplectic reversible integrators: predictor-corrector methods J. Chem. Phys. 102 8071-7
29. Mazur P and Oppenheim I 1970 Molecular theory of Brownian motion Physica 50 241-58
30. McLachlan R I and Quispel G R W 2000 Numerical integrators that contract volume Appl. Numer. Math. 34 253-60
31. Minary R, Tuckerman M and Martyna G J 2004 Long time molecular dynamics for enhanced conformational sampling in biomolecular systems J. Phys. Rev. Lett. 93 150201
32. Schutte Ch and Bornemann F A 1997 Homogenization approach to smoothed molecular dynamics Nonlinear Anal. Theory Methods Appl. 30 1805-14
33. Shub M 1987 Global Stability of Dynamical Systems (Berlin: Springer)
34. Tadmor E B, Ortiz M and Phillips R 1996 Quasicontinuum analysis of defects in solids Phil. Mag. A 73 1529-63
35. Tuckerman M E, Martyna G J and Berne B J 1992 Reversible multiple time scale molecular dynamics J. Chem. Phys. 97 1990-2001