Results 1  10
of
12
VerletI/rRESPA/Impulse Is Limited by Nonlinear Instability
 SIAM J. Sci. Comput
, 1951
"... This paper shows that in molecular dynamics (MD) when constantenergy (NVE) simulations of Newton 's equations of motion are attempted using the multiple time stepping (MTS) integrator VerletI/rRESPA/Impulse, there are nonlinear instabilities when the longest step size is a third or possibly ..."
Abstract

Cited by 13 (3 self)
 Add to MetaCart
This paper shows that in molecular dynamics (MD) when constantenergy (NVE) simulations of Newton 's equations of motion are attempted using the multiple time stepping (MTS) integrator VerletI/rRESPA/Impulse, there are nonlinear instabilities when the longest step size is a third or possibly a fourth of the period(s) of the fastest motion(s) in the system. This is demonstrated both through a thorough set of computer experiments and through the analysis of a nonlinear model problem. The numerical experiments include not only the unconstrained dynamics simulation of a droplet of flexible water and a flexible protein, but also the constrained dynamics simulation of a solvated protein, representing a range of simulation protocols commonly in use by biomolecular modelers. The observed and predicted instabilities match exactly. Previous work has identified and explained a linear instability for VerletI/rRESPA/Impulse at around half the period of the fastest motion. Mandziuk and Schlick discovered nonlinear resonances in single time stepping MD integrators, but unstable nonlinear resonances for MTS integrators are reported here for the first time. This paper also offers an explanation on the instability of MTS constrained molecular dynamics simulations of explicitly solvated proteins. More aggressive multiple step sizes are possible with mild Langevin coupling or targeted Langevin coupling, and its combination with the mollified impulse method permits step sizes 3 to 4 times larger than VerletI/rRESPA/Impulse while still retaining some accuracy.
Targeted Mollified Impulse  A Multiscale Stochastic Integrator for Long Molecular Dynamics Simulations
 SIMUL
, 2003
"... Molecular dynamics (MD) is widely used in simulations of biomolecular systems such as DNA and proteins, systems which are multiscale in nature. However, current time stepping integrators are not able to address the time scale problems. Multiscale integrators, in which the presence of "fast" ..."
Abstract

Cited by 8 (6 self)
 Add to MetaCart
Molecular dynamics (MD) is widely used in simulations of biomolecular systems such as DNA and proteins, systems which are multiscale in nature. However, current time stepping integrators are not able to address the time scale problems. Multiscale integrators, in which the presence of "fast" modes does not affect the time integration of "slow" modes, are pressingly needed in light of the fast growing biological data generated from the many genome sequencing projects. In this paper, we present a new multiple time stepping (MTS) multiscale integrator with stochasticity built in for constant temperature molecular dynamics simulations, called Targeted Mollified Impulse method (TM). TM combines the Mollified Impulse method, which is a stabler version of VerletI/rRESPA (reversible REference System Propagator Algorithm), and a selfconsistent dissipative leapfrog integrator commonly used in dissipative particle dynamics. TM introduces the Langevin coupling in a targeted manner to stabilize the MTS integrator such that the total linear momentum is conserved and less randomness in slower modes is imposed. Numerical experiments of simple model problems provide evidence that TM samples from the canonical ensemble. Possible applications include kinetics calculations such as conformational transition rates, computation of structural quantities from a canonical ensemble, and approximation of dynamical quantities from a canonical ensemble. We present results for the last two by showing that both the radial distribution functions and the selfdiffusion coefficient are correctly computed from the simulations of flexible TIP3P waters using TM with outermost time step of 16 fs and innermost time step of 2 fs. Compared to leapfrog with time step of 1 fs, the implementation of TM achieve...
Linearly scalable hybrid Monte Carlo method for conformational sampling of large biomolecules
 in SIAM Conference on Computational Science and Engineering
, 2002
"... We present a variation on the hybrid Monte Carlo (HMC) algorithm that improves the sampling of phase space. This new algorithm, called Shadow Hybrid Monte Carlo (SHMC), achieves a nearly linear scalability with system size rather than O(N ) of HMC. We tested both methods using vacuum and solva ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
(Show Context)
We present a variation on the hybrid Monte Carlo (HMC) algorithm that improves the sampling of phase space. This new algorithm, called Shadow Hybrid Monte Carlo (SHMC), achieves a nearly linear scalability with system size rather than O(N ) of HMC. We tested both methods using vacuum and solvated biological molecules. Our results show that, for example, when sampling the conformational space of a solvated Melittin with 5123 atoms, SHMC can use time steps of 0.8 fs using leapfrog, whereas HMC requires time steps of 0.05 fs to produce comparable acceptance rates (around 99%). This represents an asymptotic sixteenfold speedup in the sampling rate. The benefits could be greater for even larger systems. If # This work was supported by NSF Grant BIOCOMPLEXITYIBN0083653, NSF CAREER award ACI0135195. SH had an Arthur J. Schmitt fellowship from the University of Notre Dame.
Novel Multiscale Algorithms for Molecular Dynamics
, 2003
"... by Qun Ma In postgenomic computational biology and bioinformatics, long simulations of the dynamics of molecular systems, particularly biological molecules such as proteins and DNA, require advances in time stepping computational methods. The most severe problem of these algorithms is instability ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
by Qun Ma In postgenomic computational biology and bioinformatics, long simulations of the dynamics of molecular systems, particularly biological molecules such as proteins and DNA, require advances in time stepping computational methods. The most severe problem of these algorithms is instability. The objective of this dissertation is to present original work in constructing multiscale multiple time stepping (MTS) algorithms for molecular dynamics (MD) that allow large time steps. First, through nonlinear stability analysis and numerical experiments, we reveal that MTS integrators such as Impulse suffer nonlinear overheating when #t = T/3 or possibly #t = T/4 when constantenergy MD simulations are attempted, where #t is the longest step size and T is the shortest period of the modes in the system. Second, we present Targeted MOLLY (TM), a new multiscale integrator for MD simulations. TM combines an efficient implementation of Bspline MOLLY exploiting analytical Hessians of energies and a selfconsistent dissipative leapfrog integrator. Results show that TM allows very large time steps for slow forces (and thus multiscale) for the numerically challenging flexible TIP3P water systems (Jorgensen, et al. J. Chem. Phys., vol 79, pp 926935, 1983) while still computing the dynamical and structural properties accurately. Finally, we show yet another new MOLLY integrator, the Backward Euler (BE) MOLLY in which hydrogen bond forces can easily be included in the averaging and thus stability might be further improved.
MULTISCALE METHODS IN TIME AND SPACE FOR PARTICLE SIMULATIONS
, 2009
"... in my opinion, it ..."
(Show Context)
First Reader
, 2008
"... While molecular dynamics simulations (MD) are a fundamental method for gaining the understanding of chemical and biological systems, their computational cost is extremely high: Simulating macromolecules requires thousands of node hours and celllevel systems remain altogether out of reach. We addres ..."
Abstract
 Add to MetaCart
While molecular dynamics simulations (MD) are a fundamental method for gaining the understanding of chemical and biological systems, their computational cost is extremely high: Simulating macromolecules requires thousands of node hours and celllevel systems remain altogether out of reach. We address this issue by using an emerging mode of high performance computing that is based on configurable logic in the form of Field Programmable Gate Arrays (FPGAs). The problem is that, while FPGAs have often delivered 100fold speedups per node over microprocessorbased systems, the applications have generally been limited to those with small regular kernels operating on lowprecision integer data types. MD possesses neither. We address this problem by creating an explicitly designed FPGAcoprocessor that can be integrated into generic commercially available systems. MD is an iterative technique: the forces on each particle are computed, then applied using the equations of motion. We use standard partitioning by computing bonded forces, motion updates, and bookkeeping on the host, while computing the remaining forces (which
PROTOMOL: A Molecular Dynamics Research
 in SpringerVerlag LNCS 2659, Computational ScienceICCS 2003
, 2003
"... This paper describes the design and evaluation of PROTOMOL, a high performance objectoriented software framework for molecular dynamics (MD). ..."
Abstract
 Add to MetaCart
This paper describes the design and evaluation of PROTOMOL, a high performance objectoriented software framework for molecular dynamics (MD).
Stability of Asynchronous Variational Integrators
"... The adoption of multiple time step integrators can provide substantial computational savings for mechanical systems with multiple time scales. However, the scope of these savings may be limited by the range of allowable time step choices. In this paper we analyze the linear stability of the fully as ..."
Abstract
 Add to MetaCart
(Show Context)
The adoption of multiple time step integrators can provide substantial computational savings for mechanical systems with multiple time scales. However, the scope of these savings may be limited by the range of allowable time step choices. In this paper we analyze the linear stability of the fully asynchronous methods termed AVI, for asynchronous variational integrators. We perform a detailed analysis for the case of a onedimensional particle moving under the action of a soft and a stiff quadratic potential, integrated with two time steps in rational ratios. In this case, we provide sufficient conditions for the stability of the method. These generalize to the fully asynchronous AVI case the results obtained for synchronous multiple time stepping schemes, such as rRESPA, which show resonances when the larger time step is a multiple of the effective halfperiod of the stiff potential. Additionally, we numerically investigate the appearance of instabilities. Based on the experimental observations, we conjecture the existence of a dense set of unstable time steps when arbitrary rational ratios of time steps are considered. In this way, unstable schemes for arbitrarily small time steps can be obtained. However, the vast majority of these instabilities are extremely weak and do not present an obstacle to the
Research Projects on Hydra Multiscale Molecular Dynamics and its Applications in Nano–Fluid Dynamics and Computer–Assisted Drug Design
"... Molecular dynamics (MD) solves a system of ordinary differential equations governing the motion of the particles (atoms) in a system [2]. MD is very useful in many applications. In a biomolecular system such as solvated proteins, for example, one can use MD to study the coordinated motion of the s ..."
Abstract
 Add to MetaCart
(Show Context)
Molecular dynamics (MD) solves a system of ordinary differential equations governing the motion of the particles (atoms) in a system [2]. MD is very useful in many applications. In a biomolecular system such as solvated proteins, for example, one can use MD to study the coordinated motion of the side chains, the closing and opening of certain binding domains, the diffusion of small molecules inside the channels within the proteins, or the interaction of ligand (drug) molecules and proteins [12, 29]. These studies are crucial in providing deep insights on a molecular level as to why certain molecules are useful for regulating protein function, thereby acting as an effective drug. In a fluid system, one can use MD to study the dynamics of the fluid on a nanoscale, helping to elucidate, say, heat and mass transfer [11]. Time stepping algorithms are at the heart of molecular dynamics simulations. Even a modest improvement in time stepping algorithms will result in significant reduction in turnaround time since most MD simulations of real biological systems take days or even months to finish. A closely related technique is called coarsening. Coarsening aims at speeding up simulations by using a coarsened representation of the system, allowing a reasonable compromise between fidelity and speed. Nanodevices refer to systems that have characteristic length of less than 1 micron. Under
Extending the timescale in atomically detailed simulations
"... The current practice of molecular dynamics simulation dates back to the 1960’s and the pioneering work on smooth potential models for monatomic fluids of Rahman 1 and Verlet 2. In the 1970s, interest developed in applying molecular dynamics methods to more complicated molecular fluids such as water ..."
Abstract
 Add to MetaCart
The current practice of molecular dynamics simulation dates back to the 1960’s and the pioneering work on smooth potential models for monatomic fluids of Rahman 1 and Verlet 2. In the 1970s, interest developed in applying molecular dynamics methods to more complicated molecular fluids such as water 3,