T. Bishop, R. D. Skeel, and K. Schulten. Difficulties with multiple timestepping and the fast multipole algorithm in molecular dynamics. J. Comput. Chem., 18(14):1785--1791, Nov. 15, 1997.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....molecular dynamics applications. For example, it has been demonstrated that insufficient accuracy leads to loss of smoothness in the forces from timestep to timestep, causing instabilities in high performance molecular dynamics timestepping schemes with fast multipole evaluation of electrostatics [80,81]. It is preferable therefore to compare force evaluation methods in broader contexts. To verify the behavior of novel electrostatic treatments, energy stability throughout a dynamics simulation should be confirmed. As another measure of correctness for force evaluation methods, the short range ....

T. Bishop, R. Skeel and K. Schulten, Difficulties with multiple timestepping and the fast multipole algorithm in molecular dynamics, J. Comp. Chem., 18 (1997), pp. 1785--1791

....different MD applications [11, 48, 73] and is especially suited for parallelization [93, 95, 96, 123] However, optimized FMM codes tend to be rather elaborate. More importantly, they do not conserve energy during MD simulations unless enforcing unusual high accuracy, e.g. 12th order multi poles [10, 128]. Typically, the electrostatic problem comes with usually small distributions of mono pole moments that cause self cancellation; positive and negative charges are roughly canceled. 3.6 Other fast electrostatic methods There exist many fast electrostatic methods and implementations. Typically, ....

....multi pole method [73] MMM, O(N) is based on FMM techniques to treat periodic systems. A more detailed summary is given in [117] Finally, we mention that there exist several implementations of fast electrostatic methods that are especially adapted for multiple time stepping integrator schemes [7, 8, 10, 68, 72, 129]. 4 Parallelization A typical MD simulation is described by Algorithm 1. The work required for the numerical integration is of order O(N) which can be carried out independently for each particle. The calculation of forces scales as O(N ) due to the dominating non bonded pair wise ....

T. Bishop, R. D. Skeel, and K. Schulten. Difficulties with multiple timestepping and the fast multipole algorithm in molecular dynamics. J. Comp. Chem., 18(14):1785--1791, November 15, 1997.

....in [7] 11] 12] However, its implementation is rather expensive. In this paper, we suggest an alternative approach that modifies the force field instead of the constraint functions. This leads to a more efficient method that avoids the resonance induced instabilities of multiple time stepping [5] and the above described effect of standard constrained dynamics. 1 Introduction Classical molecular dynamics [1] leads to Hamiltonian equations of motion of type d dt q = M Gamma1 p ; d dt p = Gammar q U(q) q; p 2 R 3N , M 2 R 3N Theta3N a symmetric, positive definite mass matrix, ....

Bishop, T, Skeel, R.D., Schulten, K., Difficulties with Multiple Timestepping and the Fast Multipole Algorithm in Molecular Dynamics, submitted, 1996.

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T. Bishop, R. D. Skeel, and K. Schulten. Difficulties with multiple timestepping and the fast multipole algorithm in molecular dynamics. J. Comput. Chem., 18(14):1785--1791, Nov. 15, 1997.

.... : There is a possibility of instability if c is large, or, more specifically, if j F (q) Gamma F (q)j AE 1: That this can happen in practice is suggested by the energy growth observed in molecular dynamics if too few terms are used in the multipole expansion of the fast multipole method [3]. We can make the constant c smaller by reducing the precision . In other words, it is suggested that increasing might thwart instability 18 Acknowledgements The author is grateful to George Thiruvathukal for Fig. 1, to Amy Ryan for Figs. 2 5, and to Tony Surma for Figs. 6 9. ....

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) 1785--1791.

....Taylor expansion is significantly less accurate for the same amount of data than is centered piecewise polynomial interpolation, which can be used by a multigrid method. Moreover, for a multigrid method it is easy to ensure continuity of derivatives, which is important for stable dynamics [4]. In addition, the separation of spatial scales effected by multigrid is smoothly changing and hence can be exploited by multiple time stepping. Finally, the relative simplicity of multigrid is a definite advantage. For periodic boundaries the energy is not well defined even if the net charge is ....

T. Bishop, R. D. Skeel, and K. Schulten. Difficulties with multiple timestepping and the fast multipole algorithm in molecular dynamics. J. Comput. Chem., 18(14):1785--1791, Nov. 15, 1997.

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T. Bishop, R. D. Skeel, and K. Schulten. Difficulties with multiple timestepping and the fast multipole algorithm in molecular dynamics. J. Comp. Chem., 18(14):1785--1791, 1997.

No context found.

T. Bishop, Robert D. Skeel, and K. Schulten. Difficulties with multiple timestepping and the fast multipole algorithm in molecular dynamics. J. Comput. Chem., 18(14):1785-- 1791, November 15, 1997.

No context found.

T. Bishop, R. D. Skeel, and K. Schulten. Difficulties with multiple timestepping and the fast multipole algorithm in molecular dynamics. J. Comp. Chem., 18(14):1785--1791, Nov. 15, 1997.

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