TY - JOUR

T1 - Spatially correlated noise and variance minimization in stochastic simulations

AU - Kupferman, Raz

AU - Shamai, Yossi

PY - 2009/3

Y1 - 2009/3

N2 - Brownian simulation methods have become a popular approach in computational rheology with the introduction of the CONNFFESSIT algorithm and the method of Brownian configuration fields in the 1990s. Jourdain et al. [B. Jourdain, C.L. Bris, T. Lelievre, On a variance reduction technique for micro-macro simulations of polymeric fluids, J. Non-Newton. Fluid Mech. 122 (2004) 91-106] pointed out that both methods can be viewed as variants that differ in the spatial correlation of the noise, which can be viewed as a computational parameter for statistical error minimization. We formulate an optimization problem of variance minimization with respect to the choice of noise correlation. Our analysis takes place in an infinite-dimensional function space. We solve the optimization problem analytically for the shear flow of a Hookean dumbbell model at steady state. Interestingly, we find that spatially uncorrelated noise, i.e., CONNFFESSIT minimizes the statistical error, although the precise meaning of this statement can only be interpreted as a limit of finite-dimensional approximations.

AB - Brownian simulation methods have become a popular approach in computational rheology with the introduction of the CONNFFESSIT algorithm and the method of Brownian configuration fields in the 1990s. Jourdain et al. [B. Jourdain, C.L. Bris, T. Lelievre, On a variance reduction technique for micro-macro simulations of polymeric fluids, J. Non-Newton. Fluid Mech. 122 (2004) 91-106] pointed out that both methods can be viewed as variants that differ in the spatial correlation of the noise, which can be viewed as a computational parameter for statistical error minimization. We formulate an optimization problem of variance minimization with respect to the choice of noise correlation. Our analysis takes place in an infinite-dimensional function space. We solve the optimization problem analytically for the shear flow of a Hookean dumbbell model at steady state. Interestingly, we find that spatially uncorrelated noise, i.e., CONNFFESSIT minimizes the statistical error, although the precise meaning of this statement can only be interpreted as a limit of finite-dimensional approximations.

KW - Brownian configuration fields

KW - Brownian simulation

KW - CONNFFESSIT

KW - Optimization

UR - http://www.scopus.com/inward/record.url?scp=58249142082&partnerID=8YFLogxK

U2 - 10.1016/j.jnnfm.2008.10.002

DO - 10.1016/j.jnnfm.2008.10.002

M3 - Article

AN - SCOPUS:58249142082

SN - 0377-0257

VL - 157

SP - 92

EP - 100

JO - Journal of Non-Newtonian Fluid Mechanics

JF - Journal of Non-Newtonian Fluid Mechanics

IS - 1-2

ER -