A General Implicit Splitting for Stabilizing Numerical Simulations of Itô Stochastic Differential Equations

Petersen, Wesley P.

doi:10.1137/0036142996303973

Cited by 42 publications

(40 citation statements)

References 9 publications

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“…It is not trivial to establish regularity of the generator in (1), because the diffusion is not uniformly elliptic nor are the coefficients smooth. Further discussion of splitting methods for SDEs includes [17,3,14].…”

mentioning

confidence: 99%

Splitting for Dissipative Particle Dynamics

Shardlow¹

2003

SIAM J. Sci. Comput.

135

176

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Abstract. We study numerical methods for dissipative particle dynamics, a system of stochastic differential equations for simulating particles interacting pairwise according to a soft potential at constant temperature where the total momentum is conserved. We introduce splitting methods and examine the behavior of these methods experimentally. The performance of the methods, particularly temperature control, is compared to the modified velocity Verlet method used in many previous papers.

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mentioning

confidence: 99%

Splitting for Dissipative Particle Dynamics

Shardlow¹

2003

SIAM J. Sci. Comput.

135

176

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“…These schemes have significantly better stability than the simplest explicit Euler-Maruyama method, and one of our algorithms, scheme 2S, adopted from a second order weak algorithm [24,26], shows dramatically improved accuracy in application to a standard field theory model of block copolymer melts.…”

Section: Discussionmentioning

confidence: 99%

“…One such method that utilizes this form is the general second order splitting algorithm developed by Petersen andÖttinger [24,26]. This approach is analogous to the trapezoidal method used to solve deterministic differential equations.…”

Section: Second Order Splitting (2s)mentioning

confidence: 99%

Numerical Solutions of the Complex Langevin Equations in Polymer Field Theory

Lennon¹,

Mohler²,

Ceniceros³

et al. 2008

Multiscale Model. Simul.

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Abstract. Using a diblock copolymer melt as a model system, we show that complex Langevin (CL) simulations constitute a practical method for sampling the complex weights in field theory models of polymeric fluids. Prior work has primarily focused on numerical methods for obtaining mean-field solutions-the deterministic limit of the theory. This study is the first to go beyond EulerMaruyama integration of the full stochastic CL equations. Specifically, we use analytic expressions for the linearized forces to develop improved time integration schemes for solving the nonlinear, nonlocal stochastic CL equations. These methods can decrease the computation time required by orders of magnitude. Further, we show that the spatial and temporal multiscale nature of the system can be addressed by the use of Fourier acceleration.

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“…Next, we intégrate Eq. (7) along the trajectories X(t) applying the second order (weak sense) semi-implicit scheme of [22], the stability of which has been analyzed in [23]. Thus, using the notation X" = X(t n ), Q" = Q"(X n ) and K n = K(X"), we calcúlate Q" +1 by the following splitting procedure:…”

Section: Time Integration Ofthe Micro-scale Equationsmentioning

confidence: 99%

A semi-Lagrangian micro–macro method for viscoelastic flow calculations

Prieto

Bermejo

Laso

2010

Journal of Non-Newtonian Fluid Mechanics

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ARTICLE INFO ABSTRACT Keywords:Semi-Lagrangian scheme Micro-macro Characteristics Finite elementWe present in this paper a semi-Lagrangian algorithm to calcúlate the viscoelastic flow in which a dilute polymer solution is modeled by the FENE dumbbell kinetic model. In this algorithm the material derivative operator of the Navier-Stokes equations (the macroscopic flow equations) is discretized in time by a semiLagrangian formulation of the second order backward difference formula (BDF2). This discretization leads to solving each time step a linear generalized Stokes problem. For the stochastic differential equations of the microscopic scale model, we use the second order predictor-corrector scheme proposed in [22] applied along the forward trajectories of the center of mass of the dumbbells. Important features of the algorithm are (1) the new semi-Lagrangian projection scheme; (2) the scheme to move and lócate both the mesh-points and the dumbbells; and (3) the calculation and space discretization of the polymer stress. The algorithm has been tested on the 2d 10:1 contraction benchmark problem and has proved to be accurate and stable, being able to deal with flows at high Weissenberg(Wi) numbers; specifically, by adjusting the size of the time step we obtain solutions at Wi = 444.

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A General Implicit Splitting for Stabilizing Numerical Simulations of Itô Stochastic Differential Equations

Cited by 42 publications

References 9 publications

Splitting for Dissipative Particle Dynamics

Splitting for Dissipative Particle Dynamics

Numerical Solutions of the Complex Langevin Equations in Polymer Field Theory

A semi-Lagrangian micro–macro method for viscoelastic flow calculations

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