000176073 001__ 176073
000176073 005__ 20181203022655.0
000176073 0247_ $$2doi$$a10.1016/j.jcp.2011.11.039
000176073 022__ $$a0021-9991
000176073 02470 $$2ISI$$a000301011300007
000176073 037__ $$aARTICLE
000176073 245__ $$aNumerical methods for stochastic partial differential equations with multiple scales
000176073 260__ $$c2012
000176073 269__ $$a2012
000176073 336__ $$aJournal Articles
000176073 520__ $$aA new method for solving numerically stochastic partial differential equations (SPDEs) with multiple scales is presented. The method combines a spectral method with the heterogeneous multiscale method (HMM) presented in [W. E, D. Liu, E. Vanden-Eijnden, Analysis of multiscale methods for stochastic differential equations, Commun. Pure Appl. Math., 58(11) (2005) 1544-1585]. The class of problems that we consider are SPDEs with quadratic nonlinearities that were studied in [D. Blomker, M. Hairer, G.A. Pavliotis, Multiscale analysis for stochastic partial differential equations with quadratic nonlinearities, Nonlinearity, 20(7) (2007) 1721-1744]. For such SPDEs an amplitude equation which describes the effective dynamics at long time scales can be rigorously derived for both advective and diffusive time scales. Our method, based on micro and macro solvers, allows to capture numerically the amplitude equation accurately at a cost independent of the small scales in the problem. Numerical experiments illustrate the behavior of the proposed method. (C) 2011 Elsevier Inc. All rights reserved.
000176073 6531_ $$aStochastic partial differential equations
000176073 6531_ $$aMultiscale methods
000176073 6531_ $$aAveraging
000176073 6531_ $$aHomogenization
000176073 6531_ $$aHeterogeneous multiscale method (HMM)
000176073 6531_ $$aS-Rock
000176073 6531_ $$aInterfaces
000176073 6531_ $$aClimate
000176073 700__ $$0243806$$aAbdulle, A.$$g189915
000176073 700__ $$aPavliotis, G. A.
000176073 773__ $$j231$$q2482-2497$$tJournal of Computational Physics
000176073 909C0 $$0252279$$pANMC$$xU11991
000176073 909CO $$ooai:infoscience.tind.io:176073$$pSB$$particle
000176073 917Z8 $$x189910
000176073 917Z8 $$x189910
000176073 937__ $$aEPFL-ARTICLE-176073
000176073 973__ $$aEPFL$$rREVIEWED$$sPUBLISHED
000176073 980__ $$aARTICLE