General order conditions for stochastic partitioned Runge–Kutta methods

Anmarkrud, Sverre; Debrabant, Kristian; Kværnø, Anne

doi:10.1007/s10543-017-0693-6

Cited by 8 publications

(7 citation statements)

References 30 publications

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“…These calculations agree with the result in Ref. [41], which concluded that the GJF method is weakly second-order, and extends this order property to all GJ methods. The above calculation further illuminates why it makes sense that the time scaling factors d A and d B of Eq.…”

Section: Weak Second Order Accuracy Of the Gj Methodssupporting

confidence: 91%

“…Given the close connection between BAOAB and the GJ methods, we have been able to adapt the established analysis of accuracy for the LM family [39] into the conclusion that all the GJ methods are at least weakly second order accurate in the time step for nonlinear systems, consistent with the previously published analytical result for the GJF (GJ-I) method in Ref. [41]. The weak second order accuracy for the GJ methods is also consistent with the observation made in Section V, that the GJ methods for any given time step can be described as one and the same method with different friction parameters.…”

Section: Discussionsupporting

confidence: 79%

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Bringing discrete-time Langevin splitting methods into agreement with thermodynamics

Finkelstein,

Cheng,

Fiorin

et al. 2021

Preprint

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In light of the recently published complete set of statistically correct GJ methods for discrete-time thermodynamics, we revise the differential operator splitting method for the Langevin equation in order to comply with the basic GJ thermodynamic sampling features, namely the Boltzmann distribution and Einstein diffusion, in linear systems. This revision, which is based on the introduction of time scaling along with flexibility of a discrete-time velocity attenuation parameter, provides a direct link between the ABO splitting formalism and the GJ methods. This link brings about the conclusion that any GJ method has

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Section: Weak Second Order Accuracy Of the Gj Methodssupporting

confidence: 91%

Section: Discussionsupporting

confidence: 79%

Bringing discrete-time Langevin splitting methods into agreement with thermodynamics

Finkelstein,

Cheng,

Fiorin

et al. 2021

Preprint

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“…Both G-JF and BAOAB are included as options in LAMMPS and NAMD, respectively [1,2]. The G-JF thermostat is a stochastic two-stage partitioned Runge-Kutta method [7,3] and was shown to have highly desirable configurational properties [12]; particularly, Einstein's diffusion relation holds exactly and the configurational averages for the harmonic oscillator are independent of both the time step h and the friction parameter γ.…”

Section: Background and Theorymentioning

confidence: 99%

“…Among the family of integrators described by Leimkuhler and Matthews [17], the BAOAB method is the one characterised by the smallest configurational sampling error, and the only one here considered. Both the G-JF and BAOAB methods are weakly second-order accurate [3,17] and produce the exact configurational mean, variance and co-variance of the harmonic oscillator. This important property is not produced by many other Langevin schemes [38,26].…”

Section: Introductionmentioning

confidence: 99%

Comparison of modern Langevin integrators for simulations of coarse-grained polymer melts

2019

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For a wide range of phenomena, current computational ability does not always allow for fully atomistic simulations of high-dimensional molecular systems to reach time scales of interest. Coarse-graining (CG) is an established approach to alleviate the impact of computational limits while retaining the same algorithms used in atomistic simulations. It is of importance to understand how algorithms such as Langevin integrators perform on nontrivial CG molecular systems, and in particular how large of an integration time step can be used without introducing unacceptable amounts of error into averaged quantities of interest. To investigate this, we examined three different Langevin integrators on a CG polymer melt: the recently developed BAOAB method by Leimkuhler and Matthews [17], the Grønbech-Jensen and Farago method [12], or G-JF, and the frequently used Brünger-Brooks-Karplus integrator [6], also known as BBK. We compute and analyze key statistical properties for each. Our results indicate that the three integrators perform similarly when using a small friction parameter; however, outside of this regime the use of large integration steps produces significant deviations from the predicted diffusivity and steady-state distributions for all integration methods examined with the exception of G-JF.2010 Mathematics Subject Classification. 82C31; 82C80; 82D15.

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“…B-series for stochastic differential equations (SDEs) have been developed in different contexts by several authors, [5,7,6,18,17,24,25]. A rather general framework for developing B-series for SDEs was developed and extended in [10,12,1]. This approach is independent on whether the SDE is Itô or Stratonovich and whether weak or strong convergence is considered.…”

Section: Introductionmentioning

confidence: 99%