Implicit Runge-Kutta method for molecular dynamics integration

Janežič, Dušanka; Orel, B.

doi:10.1021/ci00012a011

Cited by 29 publications

(12 citation statements)

References 1 publication

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“…In this regard, some classical force fields, for instance, CHARMM, OPLS and COMPASS, have been developed by empirically fitting quantum mechanics results to address different application scenarios. Although the calculation principle of MD simulations seems straightforward according to the above explanations, the practical performance still needs some advanced algorithms to enable the accuracy and efficiency during the solution process, such as leapfrog, Verlet, Gear predictor-corrector, and Runge–Kutta algorithms. Considering that there are a few professional software (code) programs to implement the MD simulations, hereby, the details of MD simulations theory and method are not discussed deeply, which can be referenced by the previous literature − or help manuals of software (code): LAMMPS, Gromacs, and NAMD .…”

Section: Molecular Dynamics (Md) Simulationsmentioning

confidence: 99%

Transport of Shale Gas in Microporous/Nanoporous Media: Molecular to Pore-Scale Simulations

Fan

et al. 2020

Energy Fuels

136

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As the typical unconventional reservoir, shale gas is believed to be the most promising alternative for the conventional resources in future energy patterns, attracting more and more attention throughout the world. Generally, the majority of shale gas is trapped within the tight shale rock with ultralow porosity (<10%) and ultrasmall pore size (as less as several nanometers). Thus, the accurate understanding of gas transport characteristic and its underlying mechanism through these microporous/nanoporous media is critical for the effective exploitation of shale reservoir. In this context, we present a comprehensive review on the current advances of multiscale transport simulations of shale gas in microporous/nanoporous media from molecular to pore-scale. For the gas transport in shale nanopores using molecular dynamics (MD) simulations, the structure and force parameters of various nanopore models, including organic models (graphene, carbon nanotubes, and kerogen) and inorganic models (clays, carbonate, and quartz), and flow simulation strategies (such as nonequilibrium molecular dynamics (NEMD) and Grand Canonical Monte Carlo simulations) are systematically introduced and clarified. The significant MD simulation results about gas transport characteristic in shale nanopores then are elaborated respectively for different factors, including pore size, ambient pressure, nanopore type, atomistic roughness, and pore structure, as well as multicomponent. Besides, the two-phase transport characteristic of gas and water is also discussed, considering the ubiquity of water in shale formation. For the lattice Boltzmann method (LBM) and pore network model (PNM) approaches to conduct pore-scale simulations, we briefly review its origins, modifications, and applications for gas transport simulations in a microporous/nanoporous shale matrix. Particularly, the upscaling methods to incorporate MD simulation into LBM and PNM frameworks are emphatically expounded in the light of recent attempts of MD-based pore-scale simulations. It is hoped that this Review would be helpful for the readers to build a systematical overview on the transport characteristic of shale gas in microporous/nanoporous media and subsequently accelerate the development of the shale industry.

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Section: Molecular Dynamics (Md) Simulationsmentioning

confidence: 99%

Transport of Shale Gas in Microporous/Nanoporous Media: Molecular to Pore-Scale Simulations

Fan

et al. 2020

Energy Fuels

136

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“…The problem of how to increase the time step in MD simulations can be overcome by use of symplectic methods. − …”

Section: Introductionmentioning

confidence: 99%

Split Integration Symplectic Method for Molecular Dynamics Integration

Janežič

Merzel

1997

J. Chem. Inf. Comput. Sci.

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An explicit Split Integration Symplectic Method (SISM) for molecular dynamics (MD) simulations is described. This work is an extension of an efficient symplectic integration algorithm introduced by Janežič and Merzel (J. Chem. Inf. Comput. Sci. 1995, 35, 321−326). SISM is based on splitting of the total Hamiltonian of the system into a harmonic part and the remaining part in such a way that both parts can be efficiently computed. The Hamilton equations of motion are then solved using the second order generalized leap-frog integration scheme in which the high-frequency motions are treated analytically by the normal mode analysis which is carried out only once, at the beginning of the calculation. SISM requires only one force evaluation per integration step; the computation cost per integration step is approximately the same as that of the standard leap-frog-Verlet (LFV) method, and it allows an integration time step up to an order of magnitude larger than can be used by other methods of the same order and complexity. The simulation results of selected examplesMD simulations of a model system of linear chain molecules of the form H-(-C⋮C-)2-H and a model system of flexible CO2 moleculesshow that the SISM posses long term stability and the ability to use long time steps. The approach for MD simulations described here is general and applicable to any complex system.

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“…For example, standard high-stability implicit schemes for stiff differential equations, such as implicitEuler (IE) (43,73,95) and implicit-midpoint (IM) (57), are unsatisfactory for proteins and nucleic acids at atomic resolution at large timesteps because of numerical damping (69,96,119) and resonance (57) problems, respectively. Implicit methods are also computationally expensive since solution of a nonlinear system is required at each timestep (48,49,120,121). Algorithms based on substructuring (110) require substantial tailoring and perhaps relaxation of goals (i.e.…”

Section: Strong Vibrational Coupling In Biomoleculesmentioning

confidence: 99%

“…Implicit methods are also costly because of the nonlinear minimization or linear-system subproblem at each timestep (121), and they are not likely to be competitive in general. Janežič and coworkers reported such substantial increases in complexity with their implicit symplectic RungeKutta integrator (48), even with an efficient solution process for the resulting nonlinear system. They subsequently sought greater efficiency in parallel implementations (49) [see (55) for comments].…”

Section: Implicit Schemesmentioning

confidence: 99%

BIOMOLECULAR DYNAMICS AT LONG TIMESTEPS:Bridging the Timescale Gap Between Simulation and Experimentation

Schlick

Barth

Mandziuk

1997

Annu. Rev. Biophys. Biomol. Struct.

129

117

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Innovative algorithms have been developed during the past decade for simulating Newtonian physics for macromolecules. A major goal is alleviation of the severe requirement that the integration timestep be small enough to resolve the fastest components of the motion and thus guarantee numerical stability. This timestep problem is challenging if strictly faster methods with the same all-atom resolution at small timesteps are sought. Mathematical techniques that have worked well in other multiple-timescale contexts--where the fast motions are rapidly decaying or largely decoupled from others--have not been as successful for biomolecules, where vibrational coupling is strong. This review examines general issues that limit the timestep and describes available methods (constrained, reduced-variable, implicit, symplectic, multiple-timestep, and normal-mode-based schemes). A section compares results of selected integrators for a model dipeptide, assessing physical and numerical performance. Included is our dual timestep method LN, which relies on an approximate linearization of the equations of motion every delta t interval (5 fs or less), the solution of which is obtained by explicit integration at the inner timestep delta tau (e.g., 0.5 fs). LN is computationally competitive, providing 4-5 speedup factors, and results are in good agreement, in comparison to 0.5 fs trajectories. These collective algorithmic efforts help fill the gap between the time range that can be simulated and the timespans of major biological interest (milliseconds and longer). Still, only a hierarchy of models and methods, along with experimentational improvements, will ultimately give theoretical modeling the status of partner with experiment.

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Implicit Runge-Kutta method for molecular dynamics integration

Cited by 29 publications

References 1 publication

Transport of Shale Gas in Microporous/Nanoporous Media: Molecular to Pore-Scale Simulations

Transport of Shale Gas in Microporous/Nanoporous Media: Molecular to Pore-Scale Simulations

Split Integration Symplectic Method for Molecular Dynamics Integration

BIOMOLECULAR DYNAMICS AT LONG TIMESTEPS:Bridging the Timescale Gap Between Simulation and Experimentation

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