H. Grubmuller, H. Heller, A. Windemuth, and K. Schulten. Generalized Verlet algorithm for efficient molecular dynamics simulations with long-range interactions. Molecular Simulation, 6:121--142, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....one also hopes that the low frequency force part is the computationally most expensive part, since it is evaluated less frequently. MTS is therefore a remedy to achieve better performance, but it comes with some additional computational work. A typical MTS integrator is the Verlet I r RESPA [49, 118] method, described in Algorithm 2. The method consists of splitting the force contributions on a tagged particle into fast and slow components. If these contributions are completely decoupled, it is possible to integrate the equations of motion with different time steps which are appropriate for ....

H. Grubmuller, H. Heller, A. Windemuth, and K. Schulten. Generalized Verlet algorithm for efficient molecular dynamics simulations with longrange interactions. Molecular Simulation, 6:121--142, 1991.

....decomposes the map as (R n ; P n ) 7 (R n ; P n 1=2 ) 7 (R n 1 ; P n 1=2 ) 7 (R n 1 ; P n 1 ) and uses the fact that the composition of symplectic maps is also symplectic and the Jacobian matrix of F (R) is symmetric. The Verlet method can be generalized to multiple time steps in various ways [5], most of which destroy the symplecticness. There is a way to retain symplecticness [1] which we describe for multiple stepsizes h and Nh. Suppose we express V = V hard V soft and correspondingly partition the force vector. Then define 4 R.D. Skeel, J.J. Biesiadecki Symplectic ....

....4 R.D. Skeel, J.J. Biesiadecki Symplectic integration with variable stepsize F n = F hard n NF soft n ; n a multiple of N; F hard n ; otherwise. This retains the second order accuracy of the Verlet method as well as its symplectic property. It is called the Verlet I method in [5, 1]. In order to effect variable stepsize, we do an artificial partitioning of an interaction V into a short range interaction and a smooth long range interaction. For example, consider the potential energy V (r) C r ; such as might occur due to gravitational or electrostatic attraction. We ....

H. Grubmuller, H. Heller, A. Windemuth, and K. Schulten, Generalized Verlet algorithm for efficient molecular dynamics simulations with long-range interactions, Molecular Simulation 6 (1991) 121-142.

....n = iL, i = 0; 1; N=L. Another possibility is to keep rV (q n ) constant over L steps in (11) 13) i.e. rV (q n ) rV (q k ) for k = iL and n Gamma k L. However, this leads to a non reversible discretization. For a more detailed discussion of multiple time stepping algorithms see [4]) 6 An example Consider the function W (x) K 2 x 2 sin( x) x 2 IR. Its Gaussian transform (4) is (F W ) x) K 2 x 2 exp( Gamma 1 4 2 2 ) sin( x) Thus, for 1, F W ) y) Kx 2 =2. Let us now consider the Hamiltonian H(q; p) p 2 =2 W (q) A ....

Grubmuller, H., Heller, H., Windemuth, A., and Schulten, K., Generalized Verlet algorithm for efficient molecular dynamics simulations with long-range interactions, Molec. Sim. 6, 121--142, 1991.

....p n 1=2 = p n Gamma Deltat 2 r q U(q n ) p n 1 = p n 1=2 Gamma Deltat 2 r q U(q n 1 ) However, if K i AE 1, a small step size Deltat of order ffl with ffl Gamma2 = max i=1; m K i ; has to be used. This problem can be avoided by either using multiple timestepping methods [8], 15] 4] or by replacing the bond stretching and bond angle bending modes by holonomic constraints [1] which leads to the constrained Hamiltonian system d dt q = M Gamma1 p ; 1) d dt p = Gammar q U(q) Gamma r q g(q) 2) 0 = g(q) 3) which can be discretized by the symplectic SHAKE or ....

....dynamics and implies additional long range force field evaluations per time step. However, noting that the only significant contributions to the modified constraint function g come from nearest neighborhood interactions, the potential energy U l can be split as in multiple time stepping methods [8], 15] 4] and only the nearest neighborhood interactions are included in the evaluation of g. In fact, the main disadvantage of the formulation lies in the fact that it requires the computation of the gradient of g and thus the computation of the Hessian of U . 2 A Modified Potential Energy ....

Grubmuller, H., Heller, H., Windemuth, A., and Schulten, K., Generalized Verlet Algorithm for Efficient Molecular Dynamics Simulations with LongRange Interactions, Molecular Simulations 6, 121--142, 1991.

....temporal division can be exploited by using small timesteps ( Delta ) to resolve the rapidly varying vibrational modes and larger time intervals ( Deltat) to update the costly long range forces. In the early to mid 1990s, these approaches were further developed and applied to biomolecular dynamics [6, 7, 8, 9]. Much of these developments relied on the 4 ADRIAN SANDU AND TAMAR SCHLICK rigorous and general factorization formalism (disparate timescales, masses, etc. of the r RESPA method based on the Trotter factorization [6] a special case of which is the Verlet I method [7] These methods are ....

....dynamics [6, 7, 8, 9] Much of these developments relied on the 4 ADRIAN SANDU AND TAMAR SCHLICK rigorous and general factorization formalism (disparate timescales, masses, etc. of the r RESPA method based on the Trotter factorization [6] a special case of which is the Verlet I method [7]. These methods are symplectic [3] and time reversible, and thus are intended to simulate accurately Hamiltonian dynamics. The requirement for symplecticness dictates that the slow forces be incorporated via impulses, that is only at the time of their evaluation; hence the name Impulse MTS. These ....

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H. Grubmuller, H. Heller, A. Windemuth, and K. Schulten. Generalized Verlet algorithm for efficient molecular dynamics simulations with long-range interactions. Mol. Sim., 6:121--142, 1991.

.... other applications to evaluate computer architectures [18, 26, 32] languages and compilers [7, 13, 17, 25] and software systems [10] Efforts to improve molecular dynamics performance include sequential algorithms addressing the pairlist calculation [1, 22, 30] and numerous vectorization [3, 14, 15, 29] and parallelization efforts [4, 5, 6, 11, 12, 23] A common application of a benchmark uses total time to ascertain the efficacy of an algorithm or computing system. The details about the benchmark that should be considered will vary according to the goals of the study and what is being ....

H. Grubmuller, H. Heller, A. Windemuth, and K. Schulten. Generalized verlet algorithms for efficient molecular dynamics simulations with long-range interactions. Molecular Simulation, 6:121--142, 1991.

....of Calvo and Sanz Serna [2] although results from [10] suggest otherwise for second order integrators. McLachlan and Scovel [9] presented the development of efficient symplectic variable stepsize methods as an open problem. Our approach is to apply multiple time stepping techniques to leapfrog [3,14] in a manner that effects variable stepsize, extending results first appearing in [12,16] The potential energy of the system is partitioned into parts that can be integrated using different fractions of a largest fundamental stepsize. We show how this integration stepsize can be changed while ....

H. Grubmuller, H. Heller, A. Windemuth, and K. Schulten, Generalized Verlet algorithm for efficient molecular dynamics simulations with long-range interactions, Molec. Sim. 6, 121--142, 1991.

....L = 3, H 1 (x) 1 2 U(q) H 2 (x) K(p) and H 3 (x) 1 2 U(q) 2. the Rowlands method [19] for special separable Hamiltonian systems uses H 1 (x) H 3 (x) 1 2 U(q) Gamma 1 48 h 2 U q (q) T M Gamma1 U q (q) and H 2 (x) 1 2 p T M Gamma1 p, 3. double time stepping [7, 24] uses L = 5, H 1 (x) H 5 (x) 1 2 U slow (q) 1 4 U fast (q) H 2 (x) H 4 (x) 1 2 K(p) and H 3 (x) 1 2 U fast (q) 6 430 429 428 427 426 425 424 423 422 0 200 400 600 800 1000 time (fs) 8th order 6th order Figure 5: 6th and 8th order truncations with step size ....

H. Grubmuller, H. Heller, A. Windemuth, and K. Schulten. Generalized Verlet algorithm for efficient molecular dynamics simulations with long-range interactions. Molecular Simulation, 6:121--142, 1991.

....isolate these far field interactions [Gre87] A further optimization is to, for a given particle, compute interactions with far away points less frequently since their effects fall off rapidly with distance. Such a technique is used for example in the Generalized Verlet al..gorithm described in [GHWS91] where particles are separated into distance classes and interactions with far away particles are computed less frequently. The rate construct can be used to control this iteration frequency for clusters which may be running on asynchronous processes. One may also use a specification of rates of ....

H. GrubMuller, H. Heller, A. Windemuth, and K. Schulten, "Generalized Verlet algorithm for efficient molecular dynamics simulations with long-range interactions," Molecular Simulation, vol. 6, pp. 121--142, 1991.

....timesteps for V than for V hard . We might try the following time splitting integration method: Deltat=2, V Deltat, T V hard numerically N steps of Verlet with stepsize Deltat=N Deltat=2, V Such symplectic multiple time stepping methods were discovered independently at Illinois [6, 15] and Columbia [43] Nonsymplectic MTS methods go back over 25 years in the astrophysics literature [18] and 16 years in the MD literature [42] Typical nonsymplectic MTS methods will exhibit poor behavior on long enough time intervals. On the other hand, it seems that there may be serious accuracy ....

....years in the MD literature [42] Typical nonsymplectic MTS methods will exhibit poor behavior on long enough time intervals. On the other hand, it seems that there may be serious accuracy and stability problems with symplectic MTS methods. For example, the possibility of resonance is reported in [15, 6]. And there are other concerns that do not appear in the literature. Unless these can be cleared up, it seems more prudent to use the better nonsymplectic MTS methods proposed in [15, 6, 37] IMA, LeiReiSke, November 16, 1994 12 The use of MTS with a timestep fixed for each bonded interaction is ....

[Article contains additional citation context not shown here]

Grubmuller, H., Heller, H., and Windemuth, A., and Schulten, K., Generalized Verlet algorithm for efficient molecular dynamics simulations with long-range interactions, Molecular Simulation 6, 121--142, 1991.

....timesteps for V than for V hard . We might try the following time splitting integration method: Deltat=2, V Deltat, T V hard numerically N steps of Verlet with stepsize Deltat=N Deltat=2, V Such symplectic multiple time stepping methods were discovered independently at Illinois [6, 15] and Columbia [43] Nonsymplectic MTS methods go back over 25 years in the astrophysics literature [18] and 16 years in the MD literature [42] Typical nonsymplectic MTS methods will exhibit poor behavior on long enough time intervals. On the other hand, it seems that there may be serious accuracy ....

....years in the MD literature [42] Typical nonsymplectic MTS methods will exhibit poor behavior on long enough time intervals. On the other hand, it seems that there may be serious accuracy and stability problems with symplectic MTS methods. For example, the possibility of resonance is reported in [15, 6]. And IMA, LeiReiSke, May 26, 1995 13 there are other concerns that do not appear in the literature. Unless these can be cleared up, it seems more prudent to use the better nonsymplectic MTS methods proposed in [15, 6, 37] The use of MTS with a timestep fixed for each bonded interaction is ....

[Article contains additional citation context not shown here]

Grubmuller, H., Heller, H., and Windemuth, A., and Schulten, K., Generalized Verlet algorithm for efficient molecular dynamics simulations with long-range interactions, Molecular Simulation 6, 121--142, 1991.

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Helmut Grubmuller, Helmut Heller, Andreas Windemuth, and Klaus Schulten. Generalized Verlet algorithm for efficient molecular dynamics simulations with long-range interactions. Molec. Sim., 6:121--142, 1991.

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Helmut Grubmuller, Helmut Heller, Andreas Windemuth, and Klaus Schulten. Generalized Verlet algorithm for efficient molecular dynamics simulations with long-range interactions. Mol. Sim., 6:121--142, 1991.

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H. Grubmuller, H. Heller, A. Windemuth, and K. Schulten. Generalized Verlet algorithm for efficient molecular dynamics simulations with long-range interactions. Molecular Simulation, 6:121--142, 1991.

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H. Grubmuller, H. Heller, A. Windemuth, and K. Schulten. Generalized Verlet algorithm for efficient molecular dynamics simulations with long-range interactions. Mol. Sim., 6:121--142, 1991.

No context found.

H. Grubmuller, H. Heller, A. Windemuth, and K. Schulten. Generalized Verlet algorithm for efficient molecular dynamics simulations with long-range interactions. Molecular Simulation, 6:121--142, 1991.

No context found.

H. Grubmuller, H. Heller, A. Windemuth, and K. Schulten. Generalized Verlet algorithm for efficient molecular dynamics simulations with long-range interactions. Molecular Simulation, 6:121--142, 1991.

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H. Grubmuller, H. Heller, A. Windemuth, K. Schulten, "Generalized Verlet Algorithm for Efficient Molecular Simulations with Long-Range Interactions," Mol. Sim., Vol.6, p.121, 1991.

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H. Grubmuller, H. Heller, A. Windemuth, K. Schulten, "Generalized Verlet Algorithm for Efficient Molecular Simulations with Long-Range Interactions," Mol. Sim., Vol.6, p.121, 1991.

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Grubmuller, H., Heller, H., Windemuth, A., Schulten, K., "Generalized Verlet Algorithm for Efficient Molecular Dynamics Simulations with Long-Range Interactions", Molecular Simulation, 6, p121-142, 1991.

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