Article

A stochastic Trotter integration scheme for dissipative particle dynamics

Departamento de Física Fundamental, UNED, Avda. Senda del Rey 9, 28040 Madrid, Spain
Mathematics and Computers in Simulation (Impact Factor: 0.86). 09/2006; 72:190-194. DOI: 10.1016/j.matcom.2006.05.019
Source: DBLP

ABSTRACT In this article we show in detail the derivation of an integration scheme for the dissipative particle dynamic model (DPD) using the stochastic Trotter formula [G. De Fabritiis, M. Serrano, P. Español, P.V. Coveney, Phys. A 361 (2006) 429]. We explain some subtleties due to the stochastic character of the equations and exploit analyticity in some interesting parts of the dynamics. The DPD–Trotter integrator demonstrates the inexistence of spurious spatial correlations in the radial distribution function for an ideal gas equation of state. We also compare our numerical integrator to other available DPD integration schemes.

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Available from: Pep Español, Aug 02, 2015
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    • "For example, the reversible reference system propagator algorithm (r-RESPA) [27] is widely adopted as the CGMD integrator and it greatly accelerates simulations of systems with multiple times scales and longranged forces [27] [28] [29]. Second, DPD integrators use the modified velocity Verlet integrator derived from stochastic Trotter formula [23] [30] [31], departing from usual CGMD integrators. Following the modified velocity Verlet integrator, Symeonidis et al. [25] integrated the MTS scheme to hybrid DPD models for simulating dilute polymer solutions. "
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    ABSTRACT: We developed a multiple time-stepping (MTS) algorithm for multiscale modeling of the dynamics of platelets flowing in viscous blood plasma. This MTS algorithm improves considerably the computational efficiency without significant loss of accuracy. This study of the dynamic properties of flowing platelets employs a combination of the dissipative particle dynamics (DPD) and the coarse-grained molecular dynamics (CGMD) methods to describe the dynamic microstructures of deformable platelets in response to extracellular flow-induced stresses. The disparate spatial scales between the two methods are handled by a hybrid force field interface. However, the disparity in temporal scales between the DPD and CGMD that requires time stepping at microseconds and nanoseconds respectively, represents a computational challenge that may become prohibitive. Classical MTS algorithms manage to improve computing efficiency by multi-stepping within DPD or CGMD for up to one order of magnitude of scale differential. In order to handle 3-4 orders of magnitude disparity in the temporal scales between DPD and CGMD, we introduce a new MTS scheme hybridizing DPD and CGMD by utilizing four different time stepping sizes. We advance the fluid system at the largest time step, the fluid-platelet interface at a middle timestep size, and the nonbonded and bonded potentials of the platelet structural system at two smallest timestep sizes. Additionally, we introduce parameters to study the relationship of accuracy versus computational complexities. The numerical experiments demonstrated 3000x reduction in computing time over standard MTS methods for solving the multiscale model. This MTS algorithm establishes a computationally feasible approach for solving a particle-based system at multiple scales for performing efficient multiscale simulations.
    Journal of Computational Physics 03/2015; 284:668-686. DOI:10.1016/j.jcp.2015.01.004 · 2.49 Impact Factor
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    • "This type of splitting of inertial Langevin equations is natural, but seems to have been only recently introduced in the literature (for molecular dynamics see [7] [25], for dissipative particle dynamics see [18] [19], and for inertial particles see [16]). This paper is geared towards applications in molecular dynamics where inertial Langevin integrators (including the ones cited above) have been based on generalizations of the widely used Störmer-Verlet integrator . "
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    ABSTRACT: This paper presents a Lie-Trotter splitting for inertial Langevin equations (Geometric Langevin Algorithm) and analyzes its long-time statistical properties.The splitting is defined as a composition of a vari-ational integrator with an Ornstein-Uhlenbeck flow. Assuming the exact solution and the splitting are geometrically ergodic, the paper proves the discrete invariant measure of the splitting approximates the invariant measure of inertial Langevin to within the accuracy of the variational integrator in representing the Hamiltonian. In par-ticular, if the variational integrator admits no energy error, then the method samples the invariant measure of inertial Langevin without error. Numerical validation is provided using explicit variational inte-grators with first, second, and fourth order accuracy.
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    • "This type of splitting of inertial Langevin equations is natural, but seems to have been only recently introduced in the literature (for molecular dynamics see [6] [24], for dissipative particle dynamics see [17] [18], and for inertial particles see [15]). This paper is geared towards applications in molecular dynamics where inertial Langevin integrators (including the ones cited above) have been based on generalizations of the widely used Störmer-Verlet integrator . "
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    ABSTRACT: This paper analyzes long-time statistical properties of a Lie-Trotter splitting for inertial Langevin equations. The splitting is defined as a composition of a variational integrator with an Ornstein-Uhlenbeck flow. Assuming the exact solution and the splitting are geometri-cally ergodic, the paper proves the discrete invariant measure of the splitting approximates the invariant measure of inertial Langevin to within the accuracy of the variational integrator in representing the Hamiltonian. In particular, if the variational integrator admits no energy error, then the method samples the invariant measure of iner-tial Langevin without error. Numerical validation is provided using explicit variational integrators with first, second, and fourth order ac-curacy.
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